{"title":"Lift theorems for representations of matroids over pastures","authors":"Matthew Baker , Oliver Lorscheid","doi":"10.1016/j.jctb.2024.08.004","DOIUrl":"10.1016/j.jctb.2024.08.004","url":null,"abstract":"<div><p>Pastures are a class of field-like algebraic objects which include both partial fields and hyperfields and have nice categorical properties. We prove several lift theorems for representations of matroids over pastures, including a generalization of Pendavingh and van Zwam's Lift Theorem for partial fields. By embedding the earlier theory into a more general framework, we are able to establish new results even in the case of lifts of partial fields, for example the conjecture of Pendavingh–van Zwam that their lift construction is idempotent. We give numerous applications to matroid representations, e.g. we show that, up to projective equivalence, every pair consisting of a hexagonal representation and an orientation lifts uniquely to a near-regular representation. The proofs are different from the arguments used by Pendavingh and van Zwam, relying instead on a result of Gelfand–Rybnikov–Stone inspired by Tutte's homotopy theorem.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"170 ","pages":"Pages 1-55"},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Louis Esperet , Ugo Giocanti , Clément Legrand-Duchesne
{"title":"The structure of quasi-transitive graphs avoiding a minor with applications to the domino problem","authors":"Louis Esperet , Ugo Giocanti , Clément Legrand-Duchesne","doi":"10.1016/j.jctb.2024.08.002","DOIUrl":"10.1016/j.jctb.2024.08.002","url":null,"abstract":"<div><p>An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of its automorphism group. In this paper we obtain a structure theorem for locally finite quasi-transitive graphs avoiding a minor, which is reminiscent of the Robertson-Seymour Graph Minor Structure Theorem. We prove that every locally finite quasi-transitive graph <em>G</em> avoiding a minor has a tree-decomposition whose torsos are finite or planar; moreover the tree-decomposition is canonical, i.e. invariant under the action of the automorphism group of <em>G</em>. As applications of this result, we prove the following.</p><ul><li><span>•</span><span><p>Every locally finite quasi-transitive graph attains its Hadwiger number, that is, if such a graph contains arbitrarily large clique minors, then it contains an infinite clique minor. This extends a result of Thomassen (1992) <span><span>[38]</span></span> who proved it in the (quasi-)4-connected case and suggested that this assumption could be omitted. In particular, this shows that a Cayley graph excludes a finite minor if and only if it avoids the countable clique as a minor.</p></span></li><li><span>•</span><span><p>Locally finite quasi-transitive graphs avoiding a minor are accessible (in the sense of Thomassen and Woess), which extends known results on planar graphs to any proper minor-closed family.</p></span></li><li><span>•</span><span><p>Minor-excluded finitely generated groups are accessible (in the group-theoretic sense) and finitely presented, which extends classical results on planar groups.</p></span></li><li><span>•</span><span><p>The domino problem is decidable in a minor-excluded finitely generated group if and only if the group is virtually free, which proves the minor-excluded case of a conjecture of Ballier and Stein (2018) <span><span>[7]</span></span>.</p></span></li></ul></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 561-613"},"PeriodicalIF":1.2,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The matroid of a graphing","authors":"László Lovász","doi":"10.1016/j.jctb.2024.08.001","DOIUrl":"10.1016/j.jctb.2024.08.001","url":null,"abstract":"<div><p>Graphings serve as limit objects for bounded-degree graphs. We define the “cycle matroid” of a graphing as a submodular setfunction, with values in <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, which generalizes (up to normalization) the cycle matroid of finite graphs. We prove that for a Benjamini–Schramm convergent sequence of graphs, the total rank, normalized by the number of nodes, converges to the total rank of the limit graphing.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 542-560"},"PeriodicalIF":1.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000674/pdfft?md5=528a3e8bac91d6edbcc14e05198c5db4&pid=1-s2.0-S0095895624000674-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal spread for spanning subgraphs of Dirac hypergraphs","authors":"Tom Kelly , Alp Müyesser , Alexey Pokrovskiy","doi":"10.1016/j.jctb.2024.08.006","DOIUrl":"10.1016/j.jctb.2024.08.006","url":null,"abstract":"<div><p>Let <em>G</em> and <em>H</em> be hypergraphs on <em>n</em> vertices, and suppose <em>H</em> has large enough minimum degree to necessarily contain a copy of <em>G</em> as a subgraph. We give a general method to randomly embed <em>G</em> into <em>H</em> with good “spread”. More precisely, for a wide class of <em>G</em>, we find a randomised embedding <span><math><mi>f</mi><mo>:</mo><mi>G</mi><mo>↪</mo><mi>H</mi></math></span> with the following property: for every <em>s</em>, for any partial embedding <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of <em>s</em> vertices of <em>G</em> into <em>H</em>, the probability that <em>f</em> extends <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> is at most <span><math><mi>O</mi><msup><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></math></span>. This is a common generalisation of several streams of research surrounding the classical Dirac-type problem.</p><p>For example, setting <span><math><mi>s</mi><mo>=</mo><mi>n</mi></math></span>, we obtain an asymptotically tight lower bound on the number of embeddings of <em>G</em> into <em>H</em>. This recovers and extends recent results of Glock, Gould, Joos, Kühn, and Osthus and of Montgomery and Pavez-Signé regarding enumerating Hamilton cycles in Dirac hypergraphs. Moreover, using the recent developments surrounding the Kahn–Kalai conjecture, this result implies that many Dirac-type results hold robustly, meaning <em>G</em> still embeds into <em>H</em> after a random sparsification of its edge set. This allows us to recover a recent result of Kang, Kelly, Kühn, Osthus, and Pfenninger and of Pham, Sah, Sawhney, and Simkin for perfect matchings, and obtain novel results for Hamilton cycles and factors in Dirac hypergraphs.</p><p>Notably, our randomised embedding algorithm is self-contained and does not require Szemerédi's regularity lemma or iterative absorption.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 507-541"},"PeriodicalIF":1.2,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000728/pdfft?md5=533c17ed0f6d70854b2dd9d401343fd1&pid=1-s2.0-S0095895624000728-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kruskal–Katona-type problems via the entropy method","authors":"Ting-Wei Chao , Hung-Hsun Hans Yu","doi":"10.1016/j.jctb.2024.08.003","DOIUrl":"10.1016/j.jctb.2024.08.003","url":null,"abstract":"<div><p>In this paper, we investigate several extremal combinatorics problems that ask for the maximum number of copies of a fixed subgraph given the number of edges. We call problems of this type Kruskal–Katona-type problems. Most of the problems that will be discussed in this paper are related to the joints problem. There are two main results in this paper. First, we prove that, in a 3-edge-colored graph with <em>R</em> red, <em>G</em> green, <em>B</em> blue edges, the number of rainbow triangles is at most <span><math><msqrt><mrow><mn>2</mn><mi>R</mi><mi>G</mi><mi>B</mi></mrow></msqrt></math></span>, which is sharp. Second, we give a generalization of the Kruskal–Katona theorem that implies many other previous generalizations. Both arguments use the entropy method, and the main innovation lies in a more clever argument that improves bounds given by Shearer's inequality.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 480-506"},"PeriodicalIF":1.2,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extremal spectral radius of nonregular graphs with prescribed maximum degree","authors":"Lele Liu","doi":"10.1016/j.jctb.2024.07.007","DOIUrl":"10.1016/j.jctb.2024.07.007","url":null,"abstract":"<div><p>Let <em>G</em> be a graph attaining the maximum spectral radius among all connected nonregular graphs of order <em>n</em> with maximum degree Δ. Let <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the spectral radius of <em>G</em>. A nice conjecture due to Liu et al. (2007) <span><span>[19]</span></span> asserts that<span><span><span><math><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><mfrac><mrow><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Δ</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>Δ</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>=</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span></span></span> for each fixed Δ. Concerning an important structural property of the extremal graphs <em>G</em>, Liu and Li (2008) <span><span>[17]</span></span> put forward another conjecture which states that <em>G</em> has exactly one vertex of degree strictly less than Δ. In this paper, we make progress on the two conjectures. To be precise, we disprove the first conjecture for all <span><math><mi>Δ</mi><mo>≥</mo><mn>3</mn></math></span> by showing that<span><span><span><math><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mspace></mspace><mfrac><mrow><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Δ</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>Δ</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>≤</mo><mfrac><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo>.</mo></math></span></span></span> For small Δ, we determine the precise asymptotic behavior of <span><math><mi>Δ</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. In particular, we show that <span><math><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Δ</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>Δ</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>=</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>4</mn></math></span> if <span><math><mi>Δ</mi><mo>=</mo><mn>3</mn></math></span>; and <span><math><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo></mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Δ</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>Δ</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>=</mo><msup><","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 430-479"},"PeriodicalIF":1.2,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The automorphism group of a complementary prism","authors":"Marko Orel","doi":"10.1016/j.jctb.2024.07.004","DOIUrl":"10.1016/j.jctb.2024.07.004","url":null,"abstract":"<div><p>Given a finite simple graph Γ on <em>n</em> vertices its complementary prism is the graph <span><math><mi>Γ</mi><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> that is obtained from Γ and its complement <span><math><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> by adding a perfect matching where each its edge connects two copies of the same vertex in Γ and <span><math><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span>. It generalizes the Petersen graph, which is obtained if Γ is the pentagon. The automorphism group of <span><math><mi>Γ</mi><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> is described for an arbitrary graph Γ. In particular, it is shown that the ratio between the cardinalities of the automorphism groups of <span><math><mi>Γ</mi><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> and Γ can attain only the values 1, 2, 4, and 12. It is shown that <span><math><mi>Γ</mi><mover><mrow><mi>Γ</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> is vertex-transitive if and only if Γ is vertex-transitive and self-complementary. Moreover, the complementary prism is not a Cayley graph whenever <span><math><mi>n</mi><mo>></mo><mn>1</mn></math></span>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 406-429"},"PeriodicalIF":1.2,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000637/pdfft?md5=a7e845989152de594006704697688b0c&pid=1-s2.0-S0095895624000637-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141952091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ming Chen , Jie Han , Guanghui Wang , Donglei Yang
{"title":"H-factors in graphs with small independence number","authors":"Ming Chen , Jie Han , Guanghui Wang , Donglei Yang","doi":"10.1016/j.jctb.2024.07.005","DOIUrl":"10.1016/j.jctb.2024.07.005","url":null,"abstract":"<div><p>Let <em>H</em> be an <em>h</em>-vertex graph. The vertex arboricity <span><math><mi>a</mi><mi>r</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of <em>H</em> is the least integer <em>r</em> such that <span><math><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> can be partitioned into <em>r</em> parts and each part induces a forest in <em>H</em>. We show that for sufficiently large <span><math><mi>n</mi><mo>∈</mo><mi>h</mi><mi>N</mi></math></span>, every <em>n</em>-vertex graph <em>G</em> with <span><math><mi>δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mi>max</mi><mo></mo><mrow><mo>{</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>f</mi><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mfrac><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mi>n</mi><mo>,</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mi>n</mi><mo>}</mo></mrow></math></span> and <span><math><mi>α</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>o</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contains an <em>H</em>-factor, where <span><math><mi>f</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>a</mi><mi>r</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> or <span><math><mn>2</mn><mi>a</mi><mi>r</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>−</mo><mn>1</mn></math></span>. The result can be viewed an analogue of the Alon–Yuster theorem <span><span>[1]</span></span> in Ramsey–Turán theory, which generalizes the results of Balogh–Molla–Sharifzadeh <span><span>[2]</span></span> and Knierim–Su <span><span>[21]</span></span> on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs <em>H</em> which are not cliques.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 373-405"},"PeriodicalIF":1.2,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141952090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A weak box-perfect graph theorem","authors":"Patrick Chervet , Roland Grappe","doi":"10.1016/j.jctb.2024.07.006","DOIUrl":"10.1016/j.jctb.2024.07.006","url":null,"abstract":"<div><p>A graph <em>G</em> is called <em>perfect</em> if <span><math><mi>ω</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>=</mo><mi>χ</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> for every induced subgraph <em>H</em> of <em>G</em>, where <span><math><mi>ω</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> is the clique number of <em>H</em> and <span><math><mi>χ</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> its chromatic number. The Weak Perfect Graph Theorem of Lovász states that a graph <em>G</em> is perfect if and only if its complement <span><math><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover></math></span> is perfect. This does not hold for box-perfect graphs, which are the perfect graphs whose stable set polytope is box-totally dual integral.</p><p>We prove that both <em>G</em> and <span><math><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover></math></span> are box-perfect if and only if <span><math><msup><mrow><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover></mrow><mrow><mo>+</mo></mrow></msup></math></span> is box-perfect, where <span><math><msup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> is obtained by adding a universal vertex to <em>G</em>. Consequently, <span><math><msup><mrow><mi>G</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> is box-perfect if and only if <span><math><msup><mrow><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover></mrow><mrow><mo>+</mo></mrow></msup></math></span> is box-perfect. As a corollary, we characterize when the complete join of two graphs is box-perfect.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 367-372"},"PeriodicalIF":1.2,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0095895624000650/pdfft?md5=353ef0de641409c4b03042060f5fe02a&pid=1-s2.0-S0095895624000650-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141952089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boundary rigidity of CAT(0) cube complexes","authors":"Jérémie Chalopin, Victor Chepoi","doi":"10.1016/j.jctb.2024.07.003","DOIUrl":"10.1016/j.jctb.2024.07.003","url":null,"abstract":"<div><p>In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave, Scott, Tamitegama, and Tan (2023). The reconstruction of a finite cell complex from the boundary distances is the discrete version of the boundary rigidity problem, which is a classical problem from Riemannian geometry. In the proof, we use the bijection between CAT(0) cube complexes and median graphs, and corner peelings of median graphs.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"169 ","pages":"Pages 352-366"},"PeriodicalIF":1.2,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141960447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
