Journal of Graph Theory最新文献
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Extremal Results on Conflict-Free Coloring
IF 0.9
3区 数学
Sriram Bhyravarapu, Shiwali Gupta, Subrahmanyam Kalyanasundaram, Rogers Mathew
{"title":"Extremal Results on Conflict-Free Coloring","authors":"Sriram Bhyravarapu, Shiwali Gupta, Subrahmanyam Kalyanasundaram, Rogers Mathew","doi":"10.1002/jgt.23223","DOIUrl":"https://doi.org/10.1002/jgt.23223","url":null,"abstract":"<div>\u0000 \u0000 <p>A conflict-free open neighborhood (CFON) coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the smallest number of colors required for such a coloring is called the CFON chromatic number and is denoted by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 \u0000 <mi>ON</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free (CF) closed neighborhood (CFCN) coloring, and CFCN chromatic number (denoted by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 \u0000 <mi>CN</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>). The notion of CF coloring was introduced in 2002, and has since received considerable attention. We study CFON and CFCN colorings and show the following results. In what follows, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> denotes the maximum degree of the graph.\u0000\u0000 </p><ul>\u0000 \u0000 <li>\u0000 <p>We show that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 3","pages":"259-268"},"PeriodicalIF":0.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The Polynomial Method for Three-Path Extendability of List Colourings of Planar Graphs
平面图表着色三路可拓的多项式方法
IF 0.9
3区 数学
Przemysław Gordinowicz, Paweł Twardowski
{"title":"The Polynomial Method for Three-Path Extendability of List Colourings of Planar Graphs","authors":"Przemysław Gordinowicz, Paweł Twardowski","doi":"10.1002/jgt.23214","DOIUrl":"https://doi.org/10.1002/jgt.23214","url":null,"abstract":"<div>\u0000 \u0000 <p>We restate Thomassen's theorem of 3-extendability (Thomassen, Journal of Combinatorial Theory Series B, 97, 571–583), an extension of the famous planar 5-choosability theorem, in terms of graph polynomials. This yields an Alon–Tarsi equivalent of 3-extendability.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"237-254"},"PeriodicalIF":0.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Multigraph Overfull Conjecture
关于多图过满猜想
IF 0.9
3区 数学
Michael J. Plantholt, Songling Shan
{"title":"On the Multigraph Overfull Conjecture","authors":"Michael J. Plantholt, Songling Shan","doi":"10.1002/jgt.23221","DOIUrl":"https://doi.org/10.1002/jgt.23221","url":null,"abstract":"<div>\u0000 \u0000 <p>A subgraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of a multigraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is overfull if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mi>Δ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 \u0000 <mo>.</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> Analogous to the Overfull Conjecture proposed by Chetwynd and Hilton in 1986, Stiebitz et al. formed the multigraph version of the conjecture as follows: Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a multigraph with maximum multiplicity <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and maximum degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"226-236"},"PeriodicalIF":0.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest
图分解为匹配线性森林和有界线性森林的复杂性
IF 0.9
3区 数学
Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier
{"title":"The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest","authors":"Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier","doi":"10.1002/jgt.23208","DOIUrl":"https://doi.org/10.1002/jgt.23208","url":null,"abstract":"<div>\u0000 \u0000 <p>Deciding whether a graph can be edge-decomposed into a matching and a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0001\" wiley:location=\"equation/jgt23208-math-0001.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-bounded linear forest was recently shown by Campbell, Hörsch, and Moore to be nonedeterministic Polynomial time (NP)-complete for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>9</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0002\" wiley:location=\"equation/jgt23208-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>9</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>, and solvable in polynomial time for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0003\" wiley:location=\"equation/jgt23208-math-0003.png\"><mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. In the first part of this paper, we close this gap by showing that this problem is NP-complete for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0004\" wiley:location=\"equation/jgt23208-math-0004.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>3</mn>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"76-87"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Exact Results for Generalized Extremal Problems Forbidding an Even Cycle
禁止偶环的广义极值问题的精确结果
IF 0.9
3区 数学
Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu
{"title":"Exact Results for Generalized Extremal Problems Forbidding an Even Cycle","authors":"Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu","doi":"10.1002/jgt.23219","DOIUrl":"https://doi.org/10.1002/jgt.23219","url":null,"abstract":"<div>\u0000 \u0000 <p>We determine the maximum number of copies of <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> in a <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-free <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-vertex graph for all integers <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math> and sufficiently large <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>. Moreover, for <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow></math> and any integer <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>, we obtain the maximum number of cycles of length <span></span><math>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 </mrow></math> in an <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-vertex <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-free bipartite graph.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"218-225"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Maximal Degrees in Subgraphs of Kneser Graphs
Kneser图子图的极大度
IF 0.9
3区 数学
Peter Frankl, Andrey Kupavskii
{"title":"Maximal Degrees in Subgraphs of Kneser Graphs","authors":"Peter Frankl, Andrey Kupavskii","doi":"10.1002/jgt.23213","DOIUrl":"https://doi.org/10.1002/jgt.23213","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the maximum degree in nonempty-induced subgraphs of the Kneser graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>KG</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0001\" wiley:location=\"equation/jgt23213-math-0001.png\"><mrow><mrow><mi>KG</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math>. One of the main results asserts that, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0002\" wiley:location=\"equation/jgt23213-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x0003E}</mo><msub><mi>k</mi><mn>0</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>64</mn>\u0000 \u0000 <msup>\u0000 <mi>k</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0003\" wiley:location=\"equation/jgt23213-math-0003.png\"><mrow><mrow><mi>n</mi><mo>unicode{x0003E}</mo><mn>64</mn><msup><mi>k</mi><mn>2</mn></msup></mrow></mrow></math></annotation>\u0000 </semantics></math>, whenever a nonempty subgraph has <sp","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"88-96"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Ubiquity of Oriented Double Rays
论定向双射线的普遍性
IF 0.9
3区 数学
Florian Gut, Thilo Krill, Florian Reich
{"title":"On the Ubiquity of Oriented Double Rays","authors":"Florian Gut, Thilo Krill, Florian Reich","doi":"10.1002/jgt.23216","DOIUrl":"https://doi.org/10.1002/jgt.23216","url":null,"abstract":"<p>A digraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0001\" wiley:location=\"equation/jgt23216-math-0001.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is called <i>ubiquitous</i> if every digraph that contains arbitrarily many vertex-disjoint copies of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0002\" wiley:location=\"equation/jgt23216-math-0002.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> also contains infinitely many vertex-disjoint copies of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0003\" wiley:location=\"equation/jgt23216-math-0003.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>. We study oriented double rays, that is, digraphs <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23216:jgt23216-math-0004\" wiley:location=\"equation/jgt23216-math-0004.png\"><mrow><mrow><mi>H</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> whose underlying undirected graphs are double rays. Calling a vertex of an oriented double ray a turn if it has in-degree or out-degree 2, we prove that an oriented double ray with at least one turn is ubiquitous if and only if it has a (finite) odd number of turns. It remains an open problem to determine whether the consistently oriented double ray is ubiquitous.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"62-67"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23216","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Variant of the Teufl-Wagner Formula and Applications
Teufl-Wagner公式的一种变体及其应用
IF 0.9
3区 数学
Danyi Li, Weigen Yan
{"title":"A Variant of the Teufl-Wagner Formula and Applications","authors":"Danyi Li, Weigen Yan","doi":"10.1002/jgt.23220","DOIUrl":"https://doi.org/10.1002/jgt.23220","url":null,"abstract":"<div>\u0000 \u0000 <p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23220:jgt23220-math-0001\" wiley:location=\"equation/jgt23220-math-0001.png\"><mrow><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mo>*</mo>\u0000 </msup>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mo>*</mo>\u0000 </msup>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"68-75"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Balanced Independent Sets and Colorings of Hypergraphs
超图的平衡独立集与着色
IF 0.9
3区 数学
Abhishek Dhawan
{"title":"Balanced Independent Sets and Colorings of Hypergraphs","authors":"Abhishek Dhawan","doi":"10.1002/jgt.23212","DOIUrl":"https://doi.org/10.1002/jgt.23212","url":null,"abstract":"<p>A <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0001\" wiley:location=\"equation/jgt23212-math-0001.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-uniform hypergraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0002\" wiley:location=\"equation/jgt23212-math-0002.png\"><mrow><mrow><mi>H</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0003\" wiley:location=\"equation/jgt23212-math-0003.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-partite if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23212:jgt23212-math-0004\" wiley:location=\"equation/jgt23212-math-0004.png\"><mrow><mrow><mi>V</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> can be partitioned into <span></span><math>\u0000 <semant","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"43-51"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Packing Colourings in Complete Bipartite Graphs and the Inverse Problem for Correspondence Packing
完全二部图中的填充着色及对应填充的反问题
IF 0.9
3区 数学
Stijn Cambie, Rimma Hämäläinen
{"title":"Packing Colourings in Complete Bipartite Graphs and the Inverse Problem for Correspondence Packing","authors":"Stijn Cambie, Rimma Hämäläinen","doi":"10.1002/jgt.23215","DOIUrl":"https://doi.org/10.1002/jgt.23215","url":null,"abstract":"<div>\u0000 \u0000 <p>Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing. However, even for complete bipartite graphs, the list chromatic number can be arbitrarily large, and its exact determination is generally difficult. For the packing variant, this question becomes even harder. In this paper, we study the correspondence- and list-packing numbers of (asymmetric) complete bipartite graphs. In the most asymmetric cases, Latin squares come into play. Our results show that every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>z</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <msup>\u0000 <mi>Z</mi>\u0000 \u0000 <mo>+</mo>\u0000 </msup>\u0000 \u0000 <mo></mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mn>3</mn>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23215:jgt23215-math-0001\" wiley:location=\"equation/jgt23215-math-0001.png\"><mrow><mrow><mi>z</mi><mo>unicode{x02208}</mo><msup><mi mathvariant=\"double-struck\">Z</mi><mo>unicode{x0002B}</mo></msup><mo>unicode{x0005C}</mo><mrow><mo class=\"MathClass-open\">{</mo><mn>3</mn><mo class=\"MathClass-close\">}</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> can be equal to the correspondence packing number of a graph. We disprove a recent conjecture that relates the list packing number and the list flexibility number. Additionally, we improve the threshold functions for the correspondence packing variant.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"52-61"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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