Combinatorica最新文献
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Spanning Spheres in Dirac Hypergraphs
狄拉克超图中的跨球
IF 1.1
2区 数学
Freddie Illingworth, Richard Lang, Alp Müyesser, Olaf Parczyk, Amedeo Sgueglia
{"title":"Spanning Spheres in Dirac Hypergraphs","authors":"Freddie Illingworth, Richard Lang, Alp Müyesser, Olaf Parczyk, Amedeo Sgueglia","doi":"10.1007/s00493-025-00169-9","DOIUrl":"https://doi.org/10.1007/s00493-025-00169-9","url":null,"abstract":"<p>We show that a <i>k</i>-uniform hypergraph on <i>n</i> vertices has a spanning subgraph homeomorphic to the <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 3023.9 1125.3\" width=\"7.023ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"389\" xlink:href=\"#MJMATHI-6B\" y=\"0\"></use><use x=\"1133\" xlink:href=\"#MJMAIN-2212\" y=\"0\"></use><use x=\"2133\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use><use x=\"2634\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">(k - 1)</script></span>-dimensional sphere provided that <i>H</i> has no isolated vertices and each set of <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.109ex\" role=\"img\" style=\"vertical-align: -0.305ex;\" viewbox=\"0 -777 2244.9 908.2\" width=\"5.214ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6B\" y=\"0\"></use><use x=\"743\" xlink:href=\"#MJMAIN-2212\" y=\"0\"></use><use x=\"1744\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">k - 1</script></span> vertices supported by an edge is contained in at least <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.609ex\" role=\"img\" style=\"vertical-align: -0.705ex;\" viewbox=\"0 -820.1 4689.4 1123.4\" width=\"10.892ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use x=\"600\" xlink:href=\"#MJMAIN-2F\" y=\"0\"></use><use x=\"1101\" xlink:href=\"#MJMAIN-32\" y=\"0\"></use><use x=\"1823\" xlink:href=\"#MJMAIN-2B\" y=\"0\"></use><use x=\"2824\" xlink:href=\"#MJMATHI-6F\" y=\"0\"></use><use x=\"3309\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"3699\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use x=\"4299\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">n/2 + o(n)</script></span> edges. This gives a topological extension of Dirac’s theorem and asymptotically confirms a conjecture of Georgakopoulos, Haslegrave, Montgomery, and Narayanan. Unlike typical results in the area, our proof does not rely on the Absorption Method, the Regularity Lemma or the Blow-up Lemma. Instead, we use a recently introduced framework that is based on covering the vertex set of the host graph with a family of complete blow-ups.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"62 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Approximate Counting Version of the Multidimensional Szemerédi Theorem
多维szemersamedi定理的近似计数形式
IF 1.1
2区 数学
Natalie Behague, Joseph Hyde, Natasha Morrison, Jonathan A. Noel, Ashna Wright
{"title":"An Approximate Counting Version of the Multidimensional Szemerédi Theorem","authors":"Natalie Behague, Joseph Hyde, Natasha Morrison, Jonathan A. Noel, Ashna Wright","doi":"10.1007/s00493-025-00167-x","DOIUrl":"https://doi.org/10.1007/s00493-025-00167-x","url":null,"abstract":"<p>For any fixed <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 2358.1 995.9\" width=\"5.477ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-64\" y=\"0\"></use><use x=\"801\" xlink:href=\"#MJMAIN-2265\" y=\"0\"></use><use x=\"1857\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">dge 1</script></span> and subset <i>X</i> of <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.413ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -950.8 1192.7 1039.1\" width=\"2.77ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJAMS-4E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-64\" y=\"581\"></use></g></svg></span><script type=\"math/tex\">mathbb {N}^d</script></span>, let <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 2533.8 1125.3\" width=\"5.885ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-72\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"638\" xlink:href=\"#MJMATHI-58\" y=\"-213\"></use><use x=\"1154\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"1543\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use x=\"2144\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">r_X(n)</script></span> be the maximum cardinality of a subset <i>A</i> of <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.814ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -907.7 4801.7 1211.6\" width=\"11.152ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-7B\" y=\"0\"></use><use x=\"500\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use><use x=\"1001\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><use x=\"1446\" xlink:href=\"#MJMAIN-2026\" y=\"0\"></use><use x=\"2785\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><use x=\"3230\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><g transform=\"translate(3831,0)\"><use x=\"0\" xlink:href=\"#MJMAIN-7D\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"707\" xlink:href=\"#MJMATHI-64\" y=\"513\"></use></g></g></svg></span><script type=\"math/tex\">{1,dots,n}^d</script></span> which does not contain a subset of the form <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Set System Blowups
设置系统爆炸
IF 1.1
2区 数学
Ryan Alweiss
{"title":"Set System Blowups","authors":"Ryan Alweiss","doi":"10.1007/s00493-025-00163-1","DOIUrl":"https://doi.org/10.1007/s00493-025-00163-1","url":null,"abstract":"<p>We prove that given a constant <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>k</mi><mo>&#x2265;</mo><mn>2</mn></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 2356.1 995.9\" width=\"5.472ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6B\" y=\"0\"></use><use x=\"799\" xlink:href=\"#MJMAIN-2265\" y=\"0\"></use><use x=\"1855\" xlink:href=\"#MJMAIN-32\" y=\"0\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>k</mi><mo>≥</mo><mn>2</mn></math></span></span><script type=\"math/tex\">k ge 2</script></span> and a large set system <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">F</mi></mrow></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"1.912ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -735.2 829.5 823.4\" width=\"1.927ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJCAL-46\" y=\"0\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">F</mi></mrow></math></span></span><script type=\"math/tex\">mathcal {F}</script></span> of sets of size at most <i>w</i>, a typical <i>k</i>-tuple of sets <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>,</mo><mo>&#x22EF;</mo><mo>,</mo><msub><mi>S</mi><mi>k</mi></msub><mo stretchy=\"false\">)</mo></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 5158.2 1125.3\" width=\"11.98ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><g transform=\"translate(389,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-53\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"867\" xlink:href=\"#MJMAIN-31\" y=\"-213\"></use></g><use x=\"1456\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><use x=\"1902\" xlink:href=\"#MJMAIN-22EF\" y=\"0\"></use><use x=\"3241\" xlink:href","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"53 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Subdivisions and near-linear stable sets
细分与近线性稳定集
IF 1.1
2区 数学
Tung Nguyen, Alex Scott, Paul Seymour
{"title":"Subdivisions and near-linear stable sets","authors":"Tung Nguyen, Alex Scott, Paul Seymour","doi":"10.1007/s00493-025-00154-2","DOIUrl":"https://doi.org/10.1007/s00493-025-00154-2","url":null,"abstract":"<p>We prove that for every complete graph <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.213ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -735.2 1205.1 952.8\" width=\"2.799ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1201\" xlink:href=\"#MJMATHI-74\" y=\"-213\"></use></g></svg></span><script type=\"math/tex\">K_t</script></span>, all graphs <i>G</i> with no induced subgraph isomorphic to a subdivision of <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.213ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -735.2 1205.1 952.8\" width=\"2.799ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1201\" xlink:href=\"#MJMATHI-74\" y=\"-213\"></use></g></svg></span><script type=\"math/tex\">K_t</script></span> have a stable subset of size at least <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 6664.3 1125.3\" width=\"15.479ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use><use x=\"278\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"1065\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use><use x=\"1343\" xlink:href=\"#MJMAIN-2F\" y=\"0\"></use><g transform=\"translate(2010,0)\"><use xlink:href=\"#MJMAIN-70\"></use><use x=\"556\" xlink:href=\"#MJMAIN-6F\" y=\"0\"></use><use x=\"1057\" xlink:href=\"#MJMAIN-6C\" y=\"0\"></use><use x=\"1335\" xlink:href=\"#MJMAIN-79\" y=\"0\"></use><use x=\"1864\" xlink:href=\"#MJMAIN-6C\" y=\"0\"></use><use x=\"2142\" xlink:href=\"#MJMAIN-6F\" y=\"0\"></use><use x=\"2643\" xlink:href=\"#MJMAIN-67\" y=\"0\"></use></g><use x=\"5320\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use><use x=\"5599\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"6385\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">|G|/operatorname {polylog}|G|</script></span>. This is close to best possible, because for <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.209ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -733.9 2196.1 951.2\" width=\"5.101ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-74\" y=\"0\"></use><use x=\"639\" xlink:href=\"#MJMAIN-2265\" y=\"0\"></use><use x=\"1695\" xlink:href=\"#MJMAIN-37\" y=\"0\"></use><","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"62 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Signed graphs with the same even cycles
具有相同偶数环的符号图
IF 1.1
2区 数学
Bertrand Guenin, Cheolwon Heo, Irene Pivotto
{"title":"Signed graphs with the same even cycles","authors":"Bertrand Guenin, Cheolwon Heo, Irene Pivotto","doi":"10.1007/s00493-025-00160-4","DOIUrl":"https://doi.org/10.1007/s00493-025-00160-4","url":null,"abstract":"<p>Whitney proved that if two 3-connected graphs <i>G</i> and <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>G</mi><mo>&#x2032;</mo></msup></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.113ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -821.4 1081.3 909.7\" width=\"2.511ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMAIN-2032\" y=\"513\"></use></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>G</mi><mo>′</mo></msup></math></span></span><script type=\"math/tex\">G'</script></span> have the same set of cycles (or equivalently, the same set of cuts) then <span><span style=\"\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>G</mi><mo>=</mo><msup><mi>G</mi><mo>&#x2032;</mo></msup></math>' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"><svg aria-hidden=\"true\" focusable=\"false\" height=\"2.113ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -821.4 3201.9 909.7\" width=\"7.437ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"1064\" xlink:href=\"#MJMAIN-3D\" y=\"0\"></use><g transform=\"translate(2120,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1112\" xlink:href=\"#MJMAIN-2032\" y=\"513\"></use></g></g></svg><span role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>G</mi><mo>=</mo><msup><mi>G</mi><mo>′</mo></msup></math></span></span><script type=\"math/tex\">G=G'</script></span>. We characterize when two 4-connected signed graphs have the same set of even cycles, and we characterize when two 4-connected grafts have the same set of even cuts.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fractional Chromatic Number Vs. Hall Ratio
分数色数与霍尔比
IF 1.1
2区 数学
Raphael Steiner
{"title":"Fractional Chromatic Number Vs. Hall Ratio","authors":"Raphael Steiner","doi":"10.1007/s00493-025-00164-0","DOIUrl":"https://doi.org/10.1007/s00493-025-00164-0","url":null,"abstract":"<p>Given a graph <i>G</i>, its <i>Hall ratio</i> <span><span style=\"\">rho (G)=max _{Hsubseteq G}frac{|V(H)|}{alpha (H)}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"4.216ex\" role=\"img\" style=\"vertical-align: -1.507ex;\" viewbox=\"0 -1166.4 9758.2 1815.3\" width=\"22.664ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3C1\" y=\"0\"></use><use x=\"517\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"907\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"1693\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use><use x=\"2360\" xlink:href=\"#MJMAIN-3D\" y=\"0\"></use><g transform=\"translate(3417,0)\"><use xlink:href=\"#MJMAIN-6D\"></use><use x=\"833\" xlink:href=\"#MJMAIN-61\" y=\"0\"></use><use x=\"1334\" xlink:href=\"#MJMAIN-78\" y=\"0\"></use><g transform=\"translate(1862,-155)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"888\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1667\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use></g></g><g transform=\"translate(7114,0)\"><g transform=\"translate(286,0)\"><rect height=\"60\" stroke=\"none\" width=\"2237\" x=\"0\" y=\"220\"></rect><g transform=\"translate(60,568)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"278\" xlink:href=\"#MJMATHI-56\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1048\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1437\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"2326\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"2715\" xlink:href=\"#MJMAIN-7C\" y=\"0\"></use></g><g transform=\"translate(302,-422)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-3B1\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"640\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1030\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1918\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use></g></g></g></g></svg></span><script type=\"math/tex\">rho (G)=max _{Hsubseteq G}frac{|V(H)|}{alpha (H)}</script></span> forms a natural lower bound for its fractional chromatic number <span><span style=\"\">chi _f(G)</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.714ex\" role=\"img\" style=\"vertical-align: -0.806ex;\" viewbox=\"0 -821.4 2681.3 1168.4\" width=\"6.227ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3C7\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"886\" xlink:href=\"#MJMATHI-66\" y=\"-219\"></use><use x=\"1115\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"1505\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><use x=\"2291\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">chi _f(G)</script></s","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fat Minors in Finitely Presented Groups
有限呈现组中的肥胖未成年人
IF 1.1
2区 数学
Joseph Paul MacManus
{"title":"Fat Minors in Finitely Presented Groups","authors":"Joseph Paul MacManus","doi":"10.1007/s00493-025-00165-z","DOIUrl":"https://doi.org/10.1007/s00493-025-00165-z","url":null,"abstract":"<p>We show that a finitely presented group virtually admits a planar Cayley graph if and only if it is asymptotically minor-excluded, partially answering a conjecture of Georgakopoulos and Papasoglu in the affirmative.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"31 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partitioning a tournament into sub-tournaments of high connectivity
将锦标赛划分为高连通性的子锦标赛
IF 1.1
2区 数学
António Girão, Shoham Letzter
{"title":"Partitioning a tournament into sub-tournaments of high connectivity","authors":"António Girão, Shoham Letzter","doi":"10.1007/s00493-025-00161-3","DOIUrl":"https://doi.org/10.1007/s00493-025-00161-3","url":null,"abstract":"<p>We prove that there exists a constant <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"1.912ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -735.2 2268.1 823.4\" width=\"5.268ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"711\" xlink:href=\"#MJMAIN-3E\" y=\"0\"></use><use x=\"1767\" xlink:href=\"#MJMAIN-30\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">c > 0</script></span> such that the vertices of every strongly <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 2039.4 866.5\" width=\"4.737ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"655\" xlink:href=\"#MJMAIN-22C5\" y=\"0\"></use><use x=\"1156\" xlink:href=\"#MJMATHI-6B\" y=\"0\"></use><use x=\"1677\" xlink:href=\"#MJMATHI-74\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">c cdot kt</script></span>-connected tournament can be partitioned into <i>t</i> parts, each of which induces a strongly <i>k</i>-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of Kühn, Osthus and Townsend (2016).</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"38 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local h-polynomials, Uniform Triangulations and Real-rootedness
局部h多项式，一致三角剖分与实数根
IF 1.1
2区 数学
Christos A. Athanasiadis
{"title":"Local h-polynomials, Uniform Triangulations and Real-rootedness","authors":"Christos A. Athanasiadis","doi":"10.1007/s00493-025-00162-2","DOIUrl":"https://doi.org/10.1007/s00493-025-00162-2","url":null,"abstract":"<p>The local <i>h</i>-polynomial was introduced by Stanley as a fundamental enumerative invariant of a triangulation <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 833.5 866.5\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">Delta</script></span> of a simplex. This polynomial is known to have nonnegative and symmetric coefficients and is conjectured to be <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"1.909ex\" role=\"img\" style=\"vertical-align: -0.705ex;\" viewbox=\"0 -518.7 543.5 822.1\" width=\"1.262ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-3B3\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">gamma</script></span>-positive when <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.009ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -777 833.5 865.1\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">Delta</script></span> is flag. This paper shows that the local <i>h</i>-polynomial has the stronger property of being real-rooted when <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.013ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -778.3 833.5 866.5\" width=\"1.936ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-394\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">Delta</script></span> is the barycentric subdivision of an arbitrary geometric triangulation <span><span style=\"\"></span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"1.912ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -735.2 625.5 823.4\" width=\"1.453ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMAIN-393\" y=\"0\"></use></g></svg></span><script type=\"math/tex\">Gamma</script></span> of the simplex. An analogous result for edgewise subdivisions is proven. The proofs are based on a new combinatorial formula for the local <i>h</i>-polynomial of <span><span style=\"\"></span><span","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"51 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Isomorphisms Between Dense Random Graphs
稠密随机图之间的同构
IF 1.1
2区 数学
Erlang Surya, Lutz Warnke, Emily Zhu
{"title":"Isomorphisms Between Dense Random Graphs","authors":"Erlang Surya, Lutz Warnke, Emily Zhu","doi":"10.1007/s00493-025-00157-z","DOIUrl":"https://doi.org/10.1007/s00493-025-00157-z","url":null,"abstract":"<p>We consider two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities <span><span style=\"\">p_1,p_2</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"1.812ex\" role=\"img\" style=\"vertical-align: -0.606ex; margin-left: -0.089ex;\" viewbox=\"-38.5 -519.5 2398.5 780.3\" width=\"5.571ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-70\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"712\" xlink:href=\"#MJMAIN-31\" y=\"-213\"></use><use x=\"957\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><g transform=\"translate(1402,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-70\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"712\" xlink:href=\"#MJMAIN-32\" y=\"-213\"></use></g></g></svg></span><script type=\"math/tex\">p_1,p_2</script></span>. In particular, (i) we prove a sharp threshold result for the appearance of <span><span style=\"\">G_{n,p_1}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.709ex\" role=\"img\" style=\"vertical-align: -0.905ex;\" viewbox=\"0 -777 2185 1166.5\" width=\"5.075ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><g transform=\"translate(786,-150)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"600\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><g transform=\"translate(621,0)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-70\" y=\"0\"></use><use transform=\"scale(0.5)\" x=\"712\" xlink:href=\"#MJMAIN-31\" y=\"-326\"></use></g></g></g></svg></span><script type=\"math/tex\">G_{n,p_1}</script></span> as an induced subgraph of <span><span style=\"\">G_{N,p_2}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.709ex\" role=\"img\" style=\"vertical-align: -0.905ex;\" viewbox=\"0 -777 2388.7 1166.5\" width=\"5.548ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-47\" y=\"0\"></use><g transform=\"translate(786,-150)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-4E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"888\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use><g transform=\"translate(825,0)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-70\" y=\"0\"></use><use transform=\"scale(0.5)\" x=\"712\" xlink:href=\"#MJMAIN-32\" y=\"-326\"></use></g></g></g></svg></span><script type=\"math/tex\">G_{N,p_2}</script></span>, (ii) we show two-point concentration of the size of the maximum common induced subgraph of <span><span style=\"\">G_{N, p_1}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.714","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"33 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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