Journal of Graph Theory最新文献_第10页

Maximal Spectral Radius of Minimally k -(Edge)-Connected Graphs 最小k（边）连通图的最大谱半径

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-31 DOI: 10.1002/jgt.23286

Mingqing Zhai, Huiqiu Lin, Jinlong Shu

{"title":"Maximal Spectral Radius of Minimally \u0000 \u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 -(Edge)-Connected Graphs","authors":"Mingqing Zhai, Huiqiu Lin, Jinlong Shu","doi":"10.1002/jgt.23286","DOIUrl":"https://doi.org/10.1002/jgt.23286","url":null,"abstract":"<div>\u0000 \u0000 Minimally <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected graphs are the main focus of both structural and extremal graph theory. Perhaps the most heavily investigated parameter of this graph family is the number <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <msub>\u0000 <mi>V</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of vertices of degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Mader proved a tight lower bound for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <msub>\u0000 <mi>V</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, independent of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, and the order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. In 1981, inspired by matroids, Oxley discovered that in many cases, a considerably better bound can be given by using the size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> as a parameter. Along this line, Schmidt [Tight bounds for the vertices of degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in minimally <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected graphs, J.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"468-482"},"PeriodicalIF":1.0,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273069","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

Tight Bounds for Rainbow Partial F -Tiling in Edge-Colored Complete Hypergraphs 边色完全超图中彩虹部分F -平铺的紧界

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-23 DOI: 10.1002/jgt.23282

Jinghua Deng, Jianfeng Hou, Xizhi Liu, Caihong Yang

{"title":"Tight Bounds for Rainbow Partial \u0000 \u0000 \u0000 \u0000 F\u0000 \u0000 \u0000 -Tiling in Edge-Colored Complete Hypergraphs","authors":"Jinghua Deng, Jianfeng Hou, Xizhi Liu, Caihong Yang","doi":"10.1002/jgt.23282","DOIUrl":"https://doi.org/10.1002/jgt.23282","url":null,"abstract":"<div>\u0000 \u0000 For an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> satisfying <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>F</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>ar</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mi>F</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> denote the minimum integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that every edge-coloring of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mi>r</mi>\u0000 </msubsup>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> using <math>\u0000 <semantics>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"457-467"},"PeriodicalIF":1.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272679","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

Dominating K t -Models 支配K - t模型

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-22 DOI: 10.1002/jgt.23272

Freddie Illingworth, David R. Wood

{"title":"Dominating \u0000 \u0000 \u0000 \u0000 \u0000 K\u0000 t\u0000 \u0000 \u0000 \u0000 -Models","authors":"Freddie Illingworth, David R. Wood","doi":"10.1002/jgt.23272","DOIUrl":"https://doi.org/10.1002/jgt.23272","url":null,"abstract":"A dominating <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-model in a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a sequence <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>T</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>T</mi>\u0000 \u0000 <mi>t</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of pairwise disjoint non-empty connected subgraphs of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, such that for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>⩽</mo>\u0000 \u0000 <mi>i</mi>\u0000 \u0000 <mo><</mo>\u0000 \u0000 <mi>j</mi>\u0000 \u0000 <mo>⩽</mo>\u0000 \u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> every vertex in <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>T</mi>\u0000 \u0000 <mi>j</m","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"448-456"},"PeriodicalIF":1.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272810","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 Strengthening on Consecutive Odd Cycles in Graphs of Given Minimum Degree 最小次给定图中连续奇环的一个强化

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-21 DOI: 10.1002/jgt.23281

Hao Lin, Guanghui Wang, Wenling Zhou

{"title":"A Strengthening on Consecutive Odd Cycles in Graphs of Given Minimum Degree","authors":"Hao Lin, Guanghui Wang, Wenling Zhou","doi":"10.1002/jgt.23281","DOIUrl":"https://doi.org/10.1002/jgt.23281","url":null,"abstract":"<div>\u0000 \u0000 Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every 2-connected non-bipartite graph with minimum degree at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌈</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌉</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is even. In this paper, we confirm this conjecture for any <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>N</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Moreover, we also improve some previous results about cycles of consecutive lengths.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"431-436"},"PeriodicalIF":1.0,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272670","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 Min-Bisections of Graphs 关于图的最小等分

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-21 DOI: 10.1002/jgt.23284

Jianfeng Hou, Shufei Wu

{"title":"On Min-Bisections of Graphs","authors":"Jianfeng Hou, Shufei Wu","doi":"10.1002/jgt.23284","DOIUrl":"https://doi.org/10.1002/jgt.23284","url":null,"abstract":"<div>\u0000 \u0000 A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most 1, and its size is the number of edges which go across the two parts. Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a graph with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> edges. Bollobás and Scott asked the following: What are the largest and smallest cuts that we can guarantee with bisections of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>? There are reasonable sufficient conditions such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> has bisections of size at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>c</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> for some <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. In this paper, we study the Min-Bisection problem which has arisen in numerous contexts, and initially give some sufficient conditions such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> has bisections of size at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"437-447"},"PeriodicalIF":1.0,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272671","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

Independent Domination Number of Planar Triangulations 平面三角剖分的独立支配数

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-17 DOI: 10.1002/jgt.23285

P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad

{"title":"Independent Domination Number of Planar Triangulations","authors":"P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad","doi":"10.1002/jgt.23285","DOIUrl":"https://doi.org/10.1002/jgt.23285","url":null,"abstract":"<div>\u0000 \u0000 We show that every planar triangulation on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices has a maximal independent set of size at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. This affirms a conjecture by Botler, Fernandes, and Gutiérrez (Electron. J. Comb., 2024) based on an open question of Goddard and Henning (Appl. Math. Comput., 2020). Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan (Eur. J. Comb., 1996) that every triangulated disc has a dominating set of size at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, but restricted to triangulations.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"426-430"},"PeriodicalIF":1.0,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272803","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 Spectral Erdős–Faudree–Rousseau Theorem A谱Erdős-Faudree-Rousseau定理

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-16 DOI: 10.1002/jgt.23280

Yongtao Li, Lihua Feng, Yuejian Peng

{"title":"A Spectral Erdős–Faudree–Rousseau Theorem","authors":"Yongtao Li, Lihua Feng, Yuejian Peng","doi":"10.1002/jgt.23280","DOIUrl":"https://doi.org/10.1002/jgt.23280","url":null,"abstract":"<div>\u0000 \u0000 A well-known theorem of Mantel states that every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex graph with more than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> edges contains a triangle. An interesting problem in extremal graph theory studies the minimum number of edges contained in triangles among graphs with a prescribed number of vertices and edges. Erdős, Faudree, and Rousseau (1992) showed that a graph on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices with more than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> edges contains at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"408-425"},"PeriodicalIF":1.0,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272905","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

Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs 关于无限图的链接和精益树分解的反例

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-15 DOI: 10.1002/jgt.23279

Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Max Pitz

{"title":"Counterexamples Regarding Linked and Lean Tree-Decompositions of Infinite Graphs","authors":"Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe, Max Pitz","doi":"10.1002/jgt.23279","DOIUrl":"https://doi.org/10.1002/jgt.23279","url":null,"abstract":"Kříž and Thomas showed that every (finite or infinite) graph of tree-width <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>N</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> admits a lean tree-decomposition of width <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width. In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"398-407"},"PeriodicalIF":1.0,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145273041","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

Face Sizes and the Connectivity of the Dual 脸的大小和双连通性

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-13 DOI: 10.1002/jgt.23277

Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp

{"title":"Face Sizes and the Connectivity of the Dual","authors":"Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp","doi":"10.1002/jgt.23277","DOIUrl":"https://doi.org/10.1002/jgt.23277","url":null,"abstract":"For each <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, we prove tight lower bounds on face sizes that must be present to allow 1- or 2-cuts in simple duals of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected maps. Using these bounds, we determine the smallest genus on which a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected map can have a simple dual with a 2-cut and give lower and some upper bounds for the smallest genus on which a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected map can have a simple dual with a 1-cut.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"379-391"},"PeriodicalIF":1.0,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272966","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

On Some Algorithmic and Structural Results on Flames 关于火焰的一些算法和结构结果

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-13 DOI: 10.1002/jgt.23283

Dávid Szeszlér

{"title":"On Some Algorithmic and Structural Results on Flames","authors":"Dávid Szeszlér","doi":"10.1002/jgt.23283","DOIUrl":"https://doi.org/10.1002/jgt.23283","url":null,"abstract":"A directed graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with a root node <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is called a flame if for every vertex <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> other than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> the local edge-connectivity value <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 \u0000 <mi>F</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> from <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is equal to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>ϱ</mi>\u0000 \u0000 <mi>F</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>)</mo>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 4","pages":"392-397"},"PeriodicalIF":1.0,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145272965","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