<p>An <i>inversion</i> of a tournament <span></span><math> <semantics> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> </semantics></math> is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let <span></span><math> <semantics> <mrow> <mrow> <msub> <mtext>inv</mtext> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> be the minimum length of a sequence of inversions using sets of size at most <span></span><math> <semantics> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> </semantics></math> that result in the transitive tournament. Let <span></span><math> <semantics> <mrow> <mrow> <msub> <mtext>inv</mtext> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> be the maximum of <span></span><math> <semantics> <mrow> <mrow> <msub> <mtext>inv</mtext> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> taken over <span></span><math> <semantics> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> </semantics></math>-vertex tournaments. It is well k
一个锦标赛T的反转是通过反转所有边的方向，在一些顶点集合中有两个端点。设inv k (T)为最小长度使用大小不超过k的集合的反转序列，从而导致传递比武。设inv k (n)是的最大值invk (T)代入N顶点锦标赛。众所周知，inv2 (n) =（1 + 0 (1)）) n∕4，最近由Alon等人证明Inv (n)是对象的集合(n) = n (1)+ 0 (1) 一个锦标赛T的反转是通过反转所有边的方向，在一些顶点集合中有两个端点。设inv k (T)为最小长度使用大小不超过k的集合的反转序列，从而导致传递比武。设inv k (n)是的最大值invk (T)代入N顶点锦标赛。众所周知，inv2 (n) =（1 + 0 (1)）) n∕4，最近由Alon等人证明。 其中，inv (n)是对的(n) = n (1)+ 0 (1))。在这两种极端情况下（k = 2和n），随机比赛是极端目标。证明了invk (n)不是当k≥k 0时，通过随机比赛得到，并推测Inv 3 (n)只能通过（准）随机比赛获得。 进一步证明了（1 + 0）(1); (3)N)∕N 2∈[1,12,0。
{"title":"On Tournament Inversion","authors":"Raphael Yuster","doi":"10.1002/jgt.23251","DOIUrl":"https://doi.org/10.1002/jgt.23251","url":null,"abstract":"<p>An <i>inversion</i> of a tournament <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>inv</mtext>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>T</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the minimum length of a sequence of inversions using sets of size at most <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that result in the transitive tournament. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>inv</mtext>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the maximum of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>inv</mtext>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>T</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> taken over <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex tournaments. It is well k","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"82-91"},"PeriodicalIF":0.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23251","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624602","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}
We study extensions of Turán Theorem in edge-weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey-Turán type problems. Some of our proofs are based on the method of graph Lagrangians, while the other proofs use flag algebras. Using these results, we prove several new upper bounds on the Ramsey-Turán density of cliques. Other applications of our results are in a recent paper of Balogh, Chen, McCourt, and Murley.
{"title":"Weighted Turán Theorems With Applications to Ramsey-Turán Type of Problems","authors":"József Balogh, Domagoj Bradač, Bernard Lidický","doi":"10.1002/jgt.23244","DOIUrl":"https://doi.org/10.1002/jgt.23244","url":null,"abstract":"<p>We study extensions of Turán Theorem in edge-weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey-Turán type problems. Some of our proofs are based on the method of graph Lagrangians, while the other proofs use flag algebras. Using these results, we prove several new upper bounds on the Ramsey-Turán density of cliques. Other applications of our results are in a recent paper of Balogh, Chen, McCourt, and Murley.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"59-71"},"PeriodicalIF":0.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23244","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624865","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}
Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar chordal graphs and show that all such graphs are Hamiltonian-connected. A crucial tool used in our proof is a characteristic of 1-planar 4-trees.
{"title":"4-Connected 1-Planar Chordal Graphs Are Hamiltonian-Connected","authors":"Licheng Zhang, Yuanqiu Huang, Shengxiang Lv, Fengming Dong","doi":"10.1002/jgt.23250","DOIUrl":"https://doi.org/10.1002/jgt.23250","url":null,"abstract":"<div>\u0000 \u0000 <p>Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar chordal graphs and show that all such graphs are Hamiltonian-connected. A crucial tool used in our proof is a characteristic of 1-planar 4-trees.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"72-81"},"PeriodicalIF":0.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624866","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}
In this article, we extend the duality relation between face colorings and integer flows of graphs on orientable surfaces in Tutte's flow theory to both orientable and nonorientable surfaces and study Bouchet's 6-flow conjecture from point of embeddings of graphs on surfaces. Consequently, we verify Bouchet's conjecture for a family of embedded graphs, which have a crosscap-contractible circuit.
{"title":"Signed Graphs, Nonorientable Surfaces, and Integer Flows","authors":"You Lu, Rong Luo, Cun-Quan Zhang, Zhang Zhang","doi":"10.1002/jgt.23249","DOIUrl":"https://doi.org/10.1002/jgt.23249","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we extend the duality relation between face colorings and integer flows of graphs on orientable surfaces in Tutte's flow theory to both orientable and nonorientable surfaces and study Bouchet's 6-flow conjecture from point of embeddings of graphs on surfaces. Consequently, we verify Bouchet's conjecture for a family of embedded graphs, which have a crosscap-contractible circuit.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"48-58"},"PeriodicalIF":0.9,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624818","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}
<div> <p>A <i>separating system</i> of a graph <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math> is a family <span></span><math> <semantics> <mrow> <mrow> <mi>S</mi> </mrow> </mrow> </semantics></math> of subgraphs of <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math> for which the following holds: for all distinct edges <span></span><math> <semantics> <mrow> <mrow> <mi>e</mi> </mrow> </mrow> </semantics></math> and <span></span><math> <semantics> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> </semantics></math> of <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math>, there exists an element in <span></span><math> <semantics> <mrow> <mrow> <mi>S</mi> </mrow> </mrow> </semantics></math> that contains <span></span><math> <semantics> <mrow> <mrow> <mi>e</mi> </mrow> </mrow> </semantics></math> but not <span></span><math> <semantics> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> </semantics></math>. Recently, it has been shown that every graph of order <span></span><math> <semantics> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> </semantics></math> admits a separating system consisting of <span></span><math> <semantics> <mrow> <mrow> <mn>19</mn> <mi>n</mi> </mrow> </mrow> </semantics></math> paths, improving the previous almost linear bound of <span></span><math> <semantics> <mrow> <mrow> <mi>O</
{"title":"Separating the Edges of a Graph by Cycles and by Subdivisions of \u0000 \u0000 \u0000 \u0000 \u0000 K\u0000 4","authors":"Fábio Botler, Tássio Naia","doi":"10.1002/jgt.23248","DOIUrl":"https://doi.org/10.1002/jgt.23248","url":null,"abstract":"<div>\u0000 \u0000 <p>A <i>separating system</i> of a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a family <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of subgraphs of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for which the following holds: for all distinct edges <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, there exists an element in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that contains <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> but not <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Recently, it has been shown that every graph of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admits a separating system consisting of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>19</mn>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> paths, improving the previous almost linear bound of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>O</","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"41-47"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624596","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}
Reinhard Diestel, Raphael W. Jacobs, Paul Knappe, Paul Wollan
We show that a graph contains a large wall as a strong immersion minor if and only if the graph does not admit a tree-cut decomposition of small “width”, which is measured in terms of its adhesion and the path-likeness of its torsos.
{"title":"A Grid Theorem for Strong Immersions of Walls","authors":"Reinhard Diestel, Raphael W. Jacobs, Paul Knappe, Paul Wollan","doi":"10.1002/jgt.23245","DOIUrl":"https://doi.org/10.1002/jgt.23245","url":null,"abstract":"<p>We show that a graph contains a large wall as a strong immersion minor if and only if the graph does not admit a tree-cut decomposition of small “width”, which is measured in terms of its adhesion and the path-likeness of its torsos.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"23-32"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624421","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}
<div> <p>The recognition of Pfaffian bipartite graphs in polynomial time has been obtained, but this fact is still unknown for Pfaffian nonbipartite graphs. For a path <span></span><math> <semantics> <mrow> <mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> </mrow> </mrow> </semantics></math> and a cycle <span></span><math> <semantics> <mrow> <mrow> <msub> <mi>C</mi> <mi>n</mi> </msub> </mrow> </mrow> </semantics></math>, the Pfaffian graphs of Cartesian products <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> <mo>×</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> </mrow> </mrow> </semantics></math> and <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> <mo>×</mo> <msub> <mi>C</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> </mrow> </mrow> </semantics></math> were characterized by Lu and Zhang in 2014. Recently, Li and Wang characterized the Pfaffian graph <span></span><math> <semantics> <mrow> <mrow> <mi>G</mi> <mo>×</mo> <msub> <mi>P</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mrow> </semantics></math> for <span></span><math> <semantics> <mrow>
In this paper, we are interested in some problems related to chromatic number and clique number for the class of -free graphs and prove the following the results: (a) If is a connected ()-free graph with , then either is the complement of a bipartite graph or
Ferdinand Ihringer, Paulien Jansen, Linde Lambrecht, Yannick Neyt, Daan Rijpert, Hendrik Van Maldeghem, Magali Victoor
Given a finite Lie incidence geometry, which is either a polar space of rank at least 3 or a strong parapolar space of symplectic rank at least 4 and diameter at most 4, or the parapolar space arising from the line Grassmannian of a projective space of dimension at least 4, we show that its point graph is determined by its local structure. This follows from a more general result, which classifies graphs whose local structure can vary over all local structures of the point graphs of the aforementioned geometries. In particular, this characterises the strongly regular graphs arising from the line Grassmannian of a finite projective space, from the half spin geometry related to the quadric and from the exceptional group of type by their local structure.
{"title":"Local Recognition of the Point Graphs of Some Lie Incidence Geometries","authors":"Ferdinand Ihringer, Paulien Jansen, Linde Lambrecht, Yannick Neyt, Daan Rijpert, Hendrik Van Maldeghem, Magali Victoor","doi":"10.1002/jgt.23243","DOIUrl":"https://doi.org/10.1002/jgt.23243","url":null,"abstract":"<div>\u0000 \u0000 <p>Given a finite Lie incidence geometry, which is either a polar space of rank at least 3 or a strong parapolar space of symplectic rank at least 4 and diameter at most 4, or the parapolar space arising from the line Grassmannian of a projective space of dimension at least 4, we show that its point graph is determined by its local structure. This follows from a more general result, which classifies graphs whose local structure can vary over all local structures of the point graphs of the aforementioned geometries. In particular, this characterises the strongly regular graphs arising from the line Grassmannian of a finite projective space, from the half spin geometry related to the quadric <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 \u0000 <mo>+</mo>\u0000 </msup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>10</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>q</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and from the exceptional group of type <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>E</mi>\u0000 \u0000 <mn>6</mn>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>q</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> by their local structure.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 4","pages":"518-524"},"PeriodicalIF":0.9,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144255823","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：