Journal of Graph Theory最新文献
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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
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 <p>A graph is called minimally <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tough, claw-free graphs if <span></span><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 <span></span><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
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":"<p>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 <span></span><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 <span></span><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 <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, if (and only if) <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a <span></span><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 <i>layered wheels</i>, a construction by Sintiari and Trotignon consisting of (even-hole, <span></span><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 <span></span><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
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":"<p>Given a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the unlabeled subgraphs <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. The deck of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is the multiset <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices have at most <span></span><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
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 <p>An oriented graph is a digraph whose underlying graph is simple. Bang-Jensen and Thomassé conjectured that every digraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> with arc-strong connectivity <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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
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 <p>The Ramsey Theorem says that a graph <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> contains no complete graph <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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).</p>\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
Nathan Albin, Joan Lind, Anna Melikyan, Pietro Poggi-Corradini
{"title":"Minimizing the Determinant of the Graph Laplacian","authors":"Nathan Albin, Joan Lind, Anna Melikyan, Pietro Poggi-Corradini","doi":"10.1002/jgt.23275","DOIUrl":"https://doi.org/10.1002/jgt.23275","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be bounded away from zero and for the existence of a minimizing set of weights. These conditions are given both in terms of properties of random spanning trees and in terms of a type of density on graphs. These results generalize and extend the work of Melikyan.</p>\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"337-350"},"PeriodicalIF":1.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021754","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
Spanning Plane Subgraphs of 1-Plane Graphs
生成1-平面图的平面子图
IF 1
3区 数学
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":"<p>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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>l</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that every <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>l</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-connected spanning plane subgraph.</p>","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
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 <p>For a multiset <span></span><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 <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-list assignment of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a list assignment <span></span><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}
引用次数: 0
Positive Co-Degree Density of Hypergraphs
超图的正共度密度
IF 1
3区 数学
Anastasia Halfpap, Nathan Lemons, Cory Palmer
{"title":"Positive Co-Degree Density of Hypergraphs","authors":"Anastasia Halfpap, Nathan Lemons, Cory Palmer","doi":"10.1002/jgt.23260","DOIUrl":"https://doi.org/10.1002/jgt.23260","url":null,"abstract":"<div>\u0000 \u0000 <p>The <i>minimum positive co-degree</i> of a nonempty <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, denoted <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msubsup>\u0000 <mi>δ</mi>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>+</mo>\u0000 </msubsup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, is the maximum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-set contained in a hyperedge of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, then <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is contained in at least <span></span><math>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 2","pages":"209-222"},"PeriodicalIF":1.0,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809250","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
Total Coloring Graphs With Large Maximum Degree
具有大最大度的全着色图
IF 1
3区 数学
Aseem Dalal, Jessica McDonald, Songling Shan
{"title":"Total Coloring Graphs With Large Maximum Degree","authors":"Aseem Dalal, Jessica McDonald, Songling Shan","doi":"10.1002/jgt.23268","DOIUrl":"https://doi.org/10.1002/jgt.23268","url":null,"abstract":"<div>\u0000 \u0000 <p>We prove that for any graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the total chromatic number of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is at most <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</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>2</mn>\u0000 \u0000 <mfenced>\u0000 <mfrac>\u0000 <mrow>\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 \u0000 <mo>|</mo>\u0000 </mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</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>1</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. This saves one color in comparison with the result of Hind from 1992. In particular, our result says that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mfrac>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"110 3","pages":"249-262"},"PeriodicalIF":1.0,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022037","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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