Journal of Graph Theory最新文献_第2页

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

On the Minimum Degree of Minimally t -Tough, Claw-Free Graphs 关于最小t -坚韧无爪图的最小度

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-10 DOI: 10.1002/jgt.23278

Hui Ma, Xiaomin Hu, Weihua Yang

{"title":"On the Minimum Degree of Minimally \u0000 \u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 -Tough, Claw-Free Graphs","authors":"Hui Ma, Xiaomin Hu, Weihua Yang","doi":"10.1002/jgt.23278","DOIUrl":"https://doi.org/10.1002/jgt.23278","url":null,"abstract":"<div>\u0000 \u0000 A graph is called minimally <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tough if the toughness of the graph is <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> but the removal of any edge decreases the toughness. Katona and Varga conjectured that every minimally <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tough graph has a vertex of degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌈</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>t</mi>\u0000 </mrow>\u0000 \u0000 <mo>⌉</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Matthews and Sumner proved that the toughness of any claw-free graph is always equal to half its connectivity, which implies that the toughness of a claw-free graph is always an integer or half of an integer. Katona et al. proved that this conjecture holds for minimally <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tough, claw-free graphs if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mfenced>\u0000 <mrow>\u0000 <mfrac>\u0000 <mn>1</mn>\u0000 \u0000 <mn>2</mn>\u0000 </mfrac>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, and we proved before that this is also true if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mfrac>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"366-373"},"PeriodicalIF":1.0,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022285","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

Chordal Graphs, Even-Hole-Free Graphs and Sparse Obstructions to Bounded Treewidth 弦图、偶孔图和有界树宽的稀疏障碍

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-08 DOI: 10.1002/jgt.23276

Sepehr Hajebi

{"title":"Chordal Graphs, Even-Hole-Free Graphs and Sparse Obstructions to Bounded Treewidth","authors":"Sepehr Hajebi","doi":"10.1002/jgt.23276","DOIUrl":"https://doi.org/10.1002/jgt.23276","url":null,"abstract":"Even-hole-free graphs pose a central challenge in identifying hereditary classes of bounded treewidth. We investigate this matter by presenting and studying the following conjecture: for an integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, every even-hole-free graph of large enough treewidth has an induced subgraph isomorphic to either <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> or <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, if (and only if) <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-free chordal graph. The “only if” part follows from the properties of the so-called layered wheels, a construction by Sintiari and Trotignon consisting of (even-hole, <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>)-free graphs with arbitrarily large treewidth. Alecu et al. proved recently that the conjecture holds in two special cases: (a) when <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"351-365"},"PeriodicalIF":1.0,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022009","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

Recognizing Trees From Incomplete Decks 从不完整的甲板上识别树木

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-01 DOI: 10.1002/jgt.23274

Gabriëlle Zwaneveld

{"title":"Recognizing Trees From Incomplete Decks","authors":"Gabriëlle Zwaneveld","doi":"10.1002/jgt.23274","DOIUrl":"https://doi.org/10.1002/jgt.23274","url":null,"abstract":"Given a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the unlabeled subgraphs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> are called the cards of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. The deck of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is the multiset <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>v</mi>\u0000 \u0000 <mo>:</mo>\u0000 \u0000 <mi>v</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 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Wendy Myrvold showed that a disconnected graph and a connected graph both on <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices have at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"322-336"},"PeriodicalIF":1.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23274","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021753","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

Supereulerian Oriented Graphs With Large Arc-Strong Connectivity 具有大弧强连通性的超欧拉图

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-01 DOI: 10.1002/jgt.23254

Jia Wei, Hong-Jian Lai

{"title":"Supereulerian Oriented Graphs With Large Arc-Strong Connectivity","authors":"Jia Wei, Hong-Jian Lai","doi":"10.1002/jgt.23254","DOIUrl":"https://doi.org/10.1002/jgt.23254","url":null,"abstract":"<div>\u0000 \u0000 An oriented graph is a digraph whose underlying graph is simple. Bang-Jensen and Thomassé conjectured that every digraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with arc-strong connectivity <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> at least as large as its independence number <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>α</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> must be supereulerian. We introduce max–min ditrails in a digraph and investigate the relationship between the arc-strong connectivity <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and matching number <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>α</mi>\u0000 \u0000 <mo>′</mo>\u0000 </msup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> to assure the supereulericity of an oriented graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Utilizing the max–min ditrails with the related counting arguments, it is proved that every oriented graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"298-312"},"PeriodicalIF":1.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021818","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 Ramsey-Type Theorem on Deficiency 关于亏的一个ramsey型定理

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-01 DOI: 10.1002/jgt.23271

Jin Sun, Xinmin Hou

{"title":"A Ramsey-Type Theorem on Deficiency","authors":"Jin Sun, Xinmin Hou","doi":"10.1002/jgt.23271","DOIUrl":"https://doi.org/10.1002/jgt.23271","url":null,"abstract":"<div>\u0000 \u0000 The Ramsey Theorem says that a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> has bounded order if and only if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains no complete graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> or empty graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>E</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> as its induced subgraph. The Gyárfás-Sumner conjecture states that a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> has bounded chromatic number if and only if it contains no induced subgraph isomorphic to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> or a tree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. The deficiency of a graph is the number of vertices that cannot be covered by a maximum matching. In this paper, we prove a Ramsey-type theorem for deficiency, that is, we characterize all the forbidden induced subgraphs for graphs <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with bounded deficiency. In this application, we answer a question proposed by Fujita et al. (2006).\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"313-321"},"PeriodicalIF":1.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021902","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

Minimizing the Determinant of the Graph Laplacian 最小化图的拉普拉斯行列式

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-07-01 DOI: 10.1002/jgt.23275

Nathan Albin, Joan Lind, Anna Melikyan, Pietro Poggi-Corradini

引用次数: 0

Spanning Plane Subgraphs of 1-Plane Graphs 生成1-平面图的平面子图

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-06-22 DOI: 10.1002/jgt.23273

Kenta Noguchi, Katsuhiro Ota, Yusuke Suzuki

{"title":"Spanning Plane Subgraphs of 1-Plane Graphs","authors":"Kenta Noguchi, Katsuhiro Ota, Yusuke Suzuki","doi":"10.1002/jgt.23273","DOIUrl":"https://doi.org/10.1002/jgt.23273","url":null,"abstract":"A graph drawn on the plane is called 1-plane if each edge is crossed at most once by another edge. In this paper, we show that every 4-edge-connected 1-plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many 4-connected 1-plane graphs that have no 2-connected spanning plane subgraphs. Moreover, we consider the condition of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>l</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected 1-plane graph has an <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>l</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected spanning plane subgraph.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"290-297"},"PeriodicalIF":1.0,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022311","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

Minimum Non-Chromatic- λ -Choosable Graphs 最小非色λ可选图

IF 1 3区数学

Journal of Graph Theory Pub Date : 2025-06-15 DOI: 10.1002/jgt.23267

Jialu Zhu, Xuding Zhu

{"title":"Minimum Non-Chromatic-\u0000 \u0000 \u0000 \u0000 λ\u0000 \u0000 \u0000 -Choosable Graphs","authors":"Jialu Zhu, Xuding Zhu","doi":"10.1002/jgt.23267","DOIUrl":"https://doi.org/10.1002/jgt.23267","url":null,"abstract":"<div>\u0000 \u0000 For a multiset <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of positive integers, let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mi>λ</mi>\u0000 </msub>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <msubsup>\u0000 <mo>∑</mo>\u0000 \u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mi>q</mi>\u0000 </msubsup>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mi>i</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. A <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-list assignment of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a list assignment <math>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"283-289"},"PeriodicalIF":1.0,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022308","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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