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Matching Stability for 3-Partite 3-Uniform Hypergraphs
3部3-一致超图的匹配稳定性
IF 1
3区 数学
Hongliang Lu, Xinxin Ma
{"title":"Matching Stability for 3-Partite 3-Uniform Hypergraphs","authors":"Hongliang Lu, Xinxin Ma","doi":"10.1002/jgt.70089","DOIUrl":"https://doi.org/10.1002/jgt.70089","url":null,"abstract":"<div>\u0000 \u0000 <p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>s</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be three integers such that <span></span><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> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-partite <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-uniform hypergraph with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices in each class. Aharoni (2017) showed that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1<","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"650-662"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177136","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
Hamiltonian Cycles in Tough ( P 4 ∪ P 1 ) -Free Graphs
硬（p4∪p1）自由图中的哈密顿环
IF 1
3区 数学
Songling Shan
{"title":"Hamiltonian Cycles in Tough \u0000 \u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 \u0000 P\u0000 4\u0000 \u0000 ∪\u0000 \u0000 P\u0000 1\u0000 \u0000 \u0000 )\u0000 \u0000 \u0000 \u0000 -Free Graphs","authors":"Songling Shan","doi":"10.1002/jgt.70090","DOIUrl":"https://doi.org/10.1002/jgt.70090","url":null,"abstract":"<div>\u0000 \u0000 <p>In 1973, Chvátal conjectured that there exists a constant <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>t</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>t</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-tough graph on at least three vertices is Hamiltonian. This conjecture has inspired extensive research and has been verified for several special classes of graphs. Notably, Jung in 1978 proved that every 1-tough <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-free graph on at least three vertices is Hamiltonian. However, the problem remains challenging even when restricted to graphs with no induced <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 \u0000 <mo>∪</mo>\u0000 \u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the disjoint union of a path on four vertices and a one-vertex path. In 2013, Nikoghosyan conjectured that every 1-tough <span></span><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>4</mn>\u0000 </msub>\u0000 \u0000 <mo>∪</mo>\u0000 \u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"703-721"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176925","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 Fork-Free t-Perfect Graphs
关于无叉t-完美图
IF 1
3区 数学
Yixin Cao, Shenghua Wang
{"title":"On Fork-Free t-Perfect Graphs","authors":"Yixin Cao, Shenghua Wang","doi":"10.1002/jgt.70085","DOIUrl":"https://doi.org/10.1002/jgt.70085","url":null,"abstract":"<p>In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t-perfect graphs. While a full characterization of this class remains open, important progress has been made for claw-free graphs [Bruhn and Stein, Math. Program. 2012] and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 \u0000 <mn>5</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]. We take a further step by characterizing fork-free t-perfect graphs and showing that they are strongly t-perfect and 3-colorable. We also give polynomial-time algorithms for recognizing and coloring fork-free t-perfect graphs.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"553-570"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177060","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 Minimal k -Factor-Critical Planar Graphs
最小k因子临界平面图
IF 1
3区 数学
Qiuli Li, Fuliang Lu, Heping Zhang
{"title":"On Minimal \u0000 \u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 -Factor-Critical Planar Graphs","authors":"Qiuli Li, Fuliang Lu, Heping Zhang","doi":"10.1002/jgt.70083","DOIUrl":"https://doi.org/10.1002/jgt.70083","url":null,"abstract":"<div>\u0000 \u0000 <p>A graph of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is said to be <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math><i>-factor-critical</i> (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>0</mn>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo><</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>) if the removal of any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices results in a graph with a perfect matching. A <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-factor-critical graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is <i>minimal</i> if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is not <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-factor-critical for any edge <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Favaron and Shi posed the conjecture that every minimal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"545-552"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177061","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
Density Conditions for k Vertex-Disjoint Triangles in Tripartite Graphs
三部图中k顶点不相交三角形的密度条件
IF 1
3区 数学
Mingyang Guo, Klas Markström
{"title":"Density Conditions for \u0000 \u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 Vertex-Disjoint Triangles in Tripartite Graphs","authors":"Mingyang Guo, Klas Markström","doi":"10.1002/jgt.70079","DOIUrl":"https://doi.org/10.1002/jgt.70079","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be positive integers such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a tripartite graph with parts <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>B</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>A</mi>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>B</mi>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>C</mi>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Denote the edge densities of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 \u0000 <mo>,</mo>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"634-649"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70079","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177137","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
Chromatic Ramsey Numbers and Two-Color Turán Densities
彩色拉姆齐数和双色Turán密度
IF 1
3区 数学
Maria Axenovich, Simon Gaa, Dingyuan Liu
{"title":"Chromatic Ramsey Numbers and Two-Color Turán Densities","authors":"Maria Axenovich, Simon Gaa, Dingyuan Liu","doi":"10.1002/jgt.70086","DOIUrl":"https://doi.org/10.1002/jgt.70086","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>, its 2-color Turán number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mtext>ex</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is the maximum number of edges in an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>π</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <msub>\u0000 <mi>lim</mi>\u0000 \u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"663-676"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177157","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
b -Invariant Edges in Near-Bipartite Bricks
b -近二部砖中的不变量边
IF 1
3区 数学
Yaxian Zhang, Fuliang Lu, Heping Zhang
{"title":"b\u0000 \u0000 \u0000 -Invariant Edges in Near-Bipartite Bricks","authors":"Yaxian Zhang, Fuliang Lu, Heping Zhang","doi":"10.1002/jgt.70078","DOIUrl":"https://doi.org/10.1002/jgt.70078","url":null,"abstract":"<div>\u0000 \u0000 <p>A connected graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is matching covered if it contains at least one edge and every edge lies in some perfect matching of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Lovász proved that every matching covered graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> can be uniquely decomposed into a list of bricks (nonbipartite) and braces (bipartite) up to multiple edges; we let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>b</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> denote the number of bricks. An edge <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in a matching covered graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is removable if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is also matching covered. Furthermore, a removable edge <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of a brick <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 </mro","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"595-605"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177621","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
Sparse Graphic Degree Sequences Have Planar Realizations
稀疏图形度序列具有平面实现
IF 1
3区 数学
Amotz Bar-Noy, Toni Böhnlein, David Peleg, Yingli Ran, Dror Rawitz
{"title":"Sparse Graphic Degree Sequences Have Planar Realizations","authors":"Amotz Bar-Noy, Toni Böhnlein, David Peleg, Yingli Ran, Dror Rawitz","doi":"10.1002/jgt.70081","DOIUrl":"https://doi.org/10.1002/jgt.70081","url":null,"abstract":"<div>\u0000 \u0000 <p>A sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>d</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>d</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>d</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of positive integers is <i>graphic</i> if it is the degree sequence of some simple graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, and <i>planaric</i> if it is the degree sequence of some simple planar graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. It is known that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>∑</mo>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, then <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> has a realization by a forest, hence it is trivially planaric. This condition for <span></span><math>\u0000 <semantics>\u0000 <mrow","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"571-594"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177016","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
Edge-Disjoint Spanning Trees, Eigenvalues, and Size of Graphs
边不相交生成树，特征值和图的大小
IF 1
3区 数学
Liu Chang, Shuchao Li, Minjie Zhang
{"title":"Edge-Disjoint Spanning Trees, Eigenvalues, and Size of Graphs","authors":"Liu Chang, Shuchao Li, Minjie Zhang","doi":"10.1002/jgt.70087","DOIUrl":"https://doi.org/10.1002/jgt.70087","url":null,"abstract":"<div>\u0000 \u0000 <p>The spanning tree packing number of a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, written by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>τ</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 defined as the maximum number of edge-disjoint spanning trees. The study of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>τ</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 a classic problem in graph theory, and this parameter has important application in analyzing network robustness, routing optimization, and fault tolerance. Paul Seymour motivated the academia to establish the relationship between <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>τ</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> and eigenvalues of a connected graph. Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the class of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-vertex graphs with minimum degree <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>δ</mi>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"677-702"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177158","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
An End Degree for Digraphs
有向图的终度
IF 1
3区 数学
Matthias Hamann, Karl Heuer
{"title":"An End Degree for Digraphs","authors":"Matthias Hamann, Karl Heuer","doi":"10.1002/jgt.70084","DOIUrl":"https://doi.org/10.1002/jgt.70084","url":null,"abstract":"<p>In this paper we define a degree for ends of infinite digraphs. The well-definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices dominating the end, which we denote as combined end degree. Our main result is a characterisation of the combined end degree in terms of certain sequences of vertices, which we call end-exhausting sequences. This establishes a similar, although more complex relationship as known for the combined end degree and end-defining sequences in undirected graphs.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 4","pages":"606-618"},"PeriodicalIF":1.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177339","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}
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