Journal of Graph Theory最新文献_第5页

Signed Graphs, Nonorientable Surfaces, and Integer Flows 符号图、不可定向曲面和整数流

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-16 DOI: 10.1002/jgt.23249

You Lu, Rong Luo, Cun-Quan Zhang, Zhang Zhang

引用次数: 0

Separating the Edges of a Graph by Cycles and by Subdivisions of K 4 用k4的循环和细分来分离图的边

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-10 DOI: 10.1002/jgt.23248

Fábio Botler, Tássio Naia

{"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 A separating system of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a family <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of subgraphs of <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 <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, there exists an element in <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that contains <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> but not <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 <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 <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 <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}

引用次数: 0

A Grid Theorem for Strong Immersions of Walls 墙强浸入的网格定理

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-10 DOI: 10.1002/jgt.23245

Reinhard Diestel, Raphael W. Jacobs, Paul Knappe, Paul Wollan

引用次数: 0

A Characterization on Pfaffian Graphs of Cartesian Product G × C 2 n + 1 笛卡尔积G × c2n + 1的普氏图刻画

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-10 DOI: 10.1002/jgt.23247

Wei Li, Yao Wang, Alishba Arshad, Wuyang Sun

{"title":"A Characterization on Pfaffian Graphs of Cartesian Product \u0000 \u0000 \u0000 \u0000 G\u0000 ×\u0000 \u0000 C\u0000 \u0000 2\u0000 n\u0000 +\u0000 1","authors":"Wei Li, Yao Wang, Alishba Arshad, Wuyang Sun","doi":"10.1002/jgt.23247","DOIUrl":"https://doi.org/10.1002/jgt.23247","url":null,"abstract":"<div>\u0000 \u0000 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 <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and a cycle <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the Pfaffian graphs of Cartesian products <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> were characterized by Lu and Zhang in 2014. Recently, Li and Wang characterized the Pfaffian graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for <math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"33-40"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624328","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 Graphs With No Induced P 5 or K 5 − e 关于没有诱导p5或k5−e的图

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-09 DOI: 10.1002/jgt.23240

Arnab Char, T. Karthick

{"title":"On Graphs With No Induced \u0000 \u0000 \u0000 \u0000 \u0000 P\u0000 5\u0000 \u0000 \u0000 \u0000 or \u0000 \u0000 \u0000 \u0000 \u0000 K\u0000 5\u0000 \u0000 −\u0000 e","authors":"Arnab Char, T. Karthick","doi":"10.1002/jgt.23240","DOIUrl":"https://doi.org/10.1002/jgt.23240","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we are interested in some problems related to chromatic number and clique number for the class of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>5</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>5</mn>\u0000 </msub>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>e</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-free graphs and prove the following the results: (a) If <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a connected (<math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>5</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>5</mn>\u0000 </msub>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>)-free graph with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ω</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>7</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, then either <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is the complement of a bipartite graph or <spa","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 1","pages":"5-22"},"PeriodicalIF":0.9,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624337","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

Local Recognition of the Point Graphs of Some Lie Incidence Geometries 若干Lie关联几何点图的局部识别

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-04-06 DOI: 10.1002/jgt.23243

Ferdinand Ihringer, Paulien Jansen, Linde Lambrecht, Yannick Neyt, Daan Rijpert, Hendrik Van Maldeghem, Magali Victoor

{"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 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 <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 <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.\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}

引用次数: 0

Bollobás-Erdős-Tuza Conjecture for Graphs With No Induced K s , t Bollobás-Erdős-Tuza无诱导K s， t图的猜想

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-03-30 DOI: 10.1002/jgt.23246

Xinbu Cheng, Zixiang Xu

{"title":"Bollobás-Erdős-Tuza Conjecture for Graphs With No Induced \u0000 \u0000 \u0000 \u0000 \u0000 K\u0000 \u0000 s\u0000 ,\u0000 t","authors":"Xinbu Cheng, Zixiang Xu","doi":"10.1002/jgt.23246","DOIUrl":"https://doi.org/10.1002/jgt.23246","url":null,"abstract":"<div>\u0000 \u0000 A widely open conjecture proposed by Bollobás, Erdős, and Tuza in the early 1990s states that for any <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, if the independence number <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>α</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>Ω</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, then there is a subset <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 \u0000 <mo>⊆</mo>\u0000 \u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>T</mi>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> intersects all maximum independent sets of <math>\u0000 <semantic","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 4","pages":"514-517"},"PeriodicalIF":0.9,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144255864","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

Two Stability Theorems for K ℓ + 1 r -Saturated Hypergraphs k_1 + 1r -饱和超图的两个稳定性定理

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-03-27 DOI: 10.1002/jgt.23241

Jianfeng Hou, Heng Li, Caihong Yang, Qinghou Zeng, Yixiao Zhang

{"title":"Two Stability Theorems for \u0000 \u0000 \u0000 \u0000 \u0000 K\u0000 \u0000 ℓ\u0000 +\u0000 1\u0000 \u0000 r\u0000 \u0000 \u0000 \u0000 -Saturated Hypergraphs","authors":"Jianfeng Hou, Heng Li, Caihong Yang, Qinghou Zeng, Yixiao Zhang","doi":"10.1002/jgt.23241","DOIUrl":"https://doi.org/10.1002/jgt.23241","url":null,"abstract":"<div>\u0000 \u0000 Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a family of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-uniform hypergraphs (henceforth <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-graphs). An <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-saturated <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-graph is a maximal <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-graph not containing any member of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> as a subgraph. For integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mi>r</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mi>r</mi>\u0000 </msubsup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the collection of all <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 4","pages":"492-504"},"PeriodicalIF":0.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144256611","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

New Invariants for Partitioning a Graph Into 2-Connected Subgraphs 图划分为2连通子图的新不变量

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-03-27 DOI: 10.1002/jgt.23242

Michitaka Furuya, Masaki Kashima, Katsuhiro Ota

{"title":"New Invariants for Partitioning a Graph Into 2-Connected Subgraphs","authors":"Michitaka Furuya, Masaki Kashima, Katsuhiro Ota","doi":"10.1002/jgt.23242","DOIUrl":"https://doi.org/10.1002/jgt.23242","url":null,"abstract":"<div>\u0000 \u0000 Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a graph of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. For an integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, a partition <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\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 </mrow>\u0000 </mrow>\u0000 </semantics></math> is called a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-proper partition of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> if every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>P</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>P</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> induces a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected subgraph of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. This concept was introduced by Ferrara et al., and Borozan et al. gave minimum degree conditions for the existence of a <math>\u0000 <semantics","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 4","pages":"505-513"},"PeriodicalIF":0.9,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144256585","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

Conformal Hypergraphs: Duality and Implications for the Upper Clique Transversal Problem 共形超图：对偶性及其对上团截线问题的启示

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2025-03-24 DOI: 10.1002/jgt.23238

Endre Boros, Vladimir Gurvich, Martin Milanič, Yushi Uno

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