Journal of Graph Theory最新文献
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Graph curvature and local discrepancy
图曲率和局部差异
IF 0.9
3区 数学
Paul Horn, Adam Purcilly, Alex Stevens
{"title":"Graph curvature and local discrepancy","authors":"Paul Horn, Adam Purcilly, Alex Stevens","doi":"10.1002/jgt.23176","DOIUrl":"https://doi.org/10.1002/jgt.23176","url":null,"abstract":"<p>In recent years, discrete notions of curvature have been defined and exploited to understand various geometric properties of graphs; especially regarding heat flow, and spectral properties. In this paper, we study various combinatorial properties implied by satisfying the Bakry–Émery curvature dimension inequality <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>C</mi>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>∞</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>K</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $CD(infty ,K)$</annotation>\u0000 </semantics></math>. In particular we derive a local discrepancy inequality, similar in spirit to the expander mixing lemma from spectral graph theory, which certifies a type of “local pseudo-randomness” of the edge set of the graph, for graphs satisfying a curvature lower bound. In addition, several other consequences are derived regarding graph connectivity and cycle statistics of the graph.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"337-360"},"PeriodicalIF":0.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142869195","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
Short rainbow cycles for families of matchings and triangles
短彩虹周期的家庭匹配和三角形
IF 0.9
3区 数学
He Guo
{"title":"Short rainbow cycles for families of matchings and triangles","authors":"He Guo","doi":"10.1002/jgt.23183","DOIUrl":"https://doi.org/10.1002/jgt.23183","url":null,"abstract":"<p>A generalization of the famous Caccetta–Häggkvist conjecture, suggested by Aharoni, is that any family <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 \u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal F} }}=({F}_{1},ldots ,{F}_{n})$</annotation>\u0000 </semantics></math> of sets of edges in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${K}_{n}$</annotation>\u0000 </semantics></math>, each of size <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>, has a rainbow cycle of length at most <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⌈</mo>\u0000 \u0000 <mfrac>\u0000 <mi>n</mi>\u0000 \u0000 <mi>k</mi>\u0000 </mfrac>\u0000 \u0000 <mo>⌉</mo>\u0000 </mrow>\u0000 <annotation> $lceil frac{n}{k}rceil $</annotation>\u0000 </semantics></math>. In works by the author with Aharoni and by the author with Aharoni, Berger, Chudnovsky, and Zerbib, it was shown that asymptotically this can be improved to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>log</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $O(mathrm{log}n)$</annotation>\u0000 </se","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"325-336"},"PeriodicalIF":0.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23183","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868944","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 two problems of defective choosability of graphs
论图的缺陷选择性的两个问题
IF 0.9
3区 数学
Jie Ma, Rongxing Xu, Xuding Zhu
{"title":"On two problems of defective choosability of graphs","authors":"Jie Ma, Rongxing Xu, Xuding Zhu","doi":"10.1002/jgt.23182","DOIUrl":"https://doi.org/10.1002/jgt.23182","url":null,"abstract":"<p>Given positive integers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>≥</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $pge k$</annotation>\u0000 </semantics></math>, and a nonnegative integer <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation> $d$</annotation>\u0000 </semantics></math>, we say a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>d</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $(k,d,p)$</annotation>\u0000 </semantics></math>-choosable if for every list assignment <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation> $L$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>∣</mo>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∣</mo>\u0000 <mo>≥</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $| L(v)| ge k$</annotation>\u0000 </semantics></math> for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>∈</mo>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $vin V(G)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>∣</mo>\u0000 <msub>\u0000 <mo>⋃</mo>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 <mo>∈</mo>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </msub>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"313-324"},"PeriodicalIF":0.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868925","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
d $d$ -connectivity of the random graph with restricted budget
D $ D $ -有限预算随机图的连通性
IF 0.9
3区 数学
Lyuben Lichev
{"title":"d\u0000 \u0000 $d$\u0000 -connectivity of the random graph with restricted budget","authors":"Lyuben Lichev","doi":"10.1002/jgt.23180","DOIUrl":"https://doi.org/10.1002/jgt.23180","url":null,"abstract":"<p>In this short note, we consider a graph process recently introduced by Frieze, Krivelevich and Michaeli. In their model, the edges of the complete graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${K}_{n}$</annotation>\u0000 </semantics></math> are ordered uniformly at random and are then revealed consecutively to a player called Builder. At every round, Builder must decide if they accept the edge proposed at this round or not. We prove that, for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $dge 2$</annotation>\u0000 </semantics></math>, Builder can construct a spanning <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation> $d$</annotation>\u0000 </semantics></math>-connected graph after <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mi>log</mi>\u0000 \u0000 <mo> </mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $(1+o(1))nmathrm{log}unicode{x0200A}n/2$</annotation>\u0000 </semantics></math> rounds by accepting <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"293-312"},"PeriodicalIF":0.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868961","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
Finding dense minors using average degree
利用平均程度查找密集的未成年人
IF 0.9
3区 数学
Kevin Hendrey, Sergey Norin, Raphael Steiner, Jérémie Turcotte
{"title":"Finding dense minors using average degree","authors":"Kevin Hendrey, Sergey Norin, Raphael Steiner, Jérémie Turcotte","doi":"10.1002/jgt.23169","DOIUrl":"https://doi.org/10.1002/jgt.23169","url":null,"abstract":"<p>Motivated by Hadwiger's conjecture, we study the problem of finding the densest possible <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow></math>-vertex minor in graphs of average degree at least <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow></math>. We show that if <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> has average degree at least <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow></math>, it contains a minor on <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow></math> vertices with at least <span></span><math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msqrt>\u0000 <mn>2</mn>\u0000 </msqrt>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mfenced>\u0000 <mfrac>\u0000 <mi>t</mi>\u0000 \u0000 <mn>2</mn>\u0000 </mfrac>\u0000 </mfenced>\u0000 </mrow></math> edges. We show that this cannot be improved beyond <span></span><math>\u0000 \u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mfrac>\u0000 <mn>3</mn>\u0000 \u0000 <mn>4</mn>\u0000 </mfrac>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 \u0000 <mfenced>\u0000 <mfrac>\u0000 <mi>t</mi>\u0000 \u0000 <mn>2</mn>\u0000 </mfrac>\u0000 </mfenced>\u0000 </mrow></math>. Finally, for <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>t</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"205-223"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707851","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
Compatible powers of Hamilton cycles in dense graphs
密集图中汉密尔顿循环的相容幂
IF 0.9
3区 数学
Xiaohan Cheng, Jie Hu, Donglei Yang
{"title":"Compatible powers of Hamilton cycles in dense graphs","authors":"Xiaohan Cheng, Jie Hu, Donglei Yang","doi":"10.1002/jgt.23178","DOIUrl":"10.1002/jgt.23178","url":null,"abstract":"<p>The notion of incompatibility system was first proposed by Krivelevich, Lee and Sudakov to formulate the robustness of Hamiltonicity of Dirac graphs. Given a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $G=(V,E)$</annotation>\u0000 </semantics></math>, an <i>incompatibility system</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal F} }}$</annotation>\u0000 </semantics></math> over <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a family <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <msub>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>v</mi>\u0000 </msub>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>V</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal F} }}={{{F}_{v}}}_{vin V}$</annotation>\u0000 </semantics></math> such that for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation> $vin V$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>v</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${F}_{v}$</annotation>\u0000 </semantics></math> is a family of edge pairs <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"257-273"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263967","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
Fractional factors and component factors in graphs with isolated toughness smaller than 1
孤立韧性小于 1 的图形中的分数因子和分量因子
IF 0.9
3区 数学
Isaak H. Wolf
{"title":"Fractional factors and component factors in graphs with isolated toughness smaller than 1","authors":"Isaak H. Wolf","doi":"10.1002/jgt.23179","DOIUrl":"10.1002/jgt.23179","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a simple graph and let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $n,m$</annotation>\u0000 </semantics></math> be two integers with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 \u0000 <mo><</mo>\u0000 \u0000 <mi>m</mi>\u0000 \u0000 <mo><</mo>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $0lt mlt n$</annotation>\u0000 </semantics></math>. We prove that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mi>o</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>S</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mfrac>\u0000 <mi>n</mi>\u0000 \u0000 <mi>m</mi>\u0000 </mfrac>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>S</mi>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow>\u0000 <annotation> $iso(G-S)le frac{n}{m}| S| $</annotation>\u0000 </semantics></math> for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</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 <annotation> $Ssubset V(G)$</annotation>\u0000 </semantics></math> if and only if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"274-287"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23179","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263968","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
Edge-transitive cubic graphs of twice square-free order
两倍无平方阶的边跨立方图
IF 0.9
3区 数学
Gui Xian Liu, Zai Ping Lu
{"title":"Edge-transitive cubic graphs of twice square-free order","authors":"Gui Xian Liu, Zai Ping Lu","doi":"10.1002/jgt.23168","DOIUrl":"10.1002/jgt.23168","url":null,"abstract":"<p>A graph is edge-transitive if its automorphism group acts transitively on the edge set. This paper presents a complete classification for connected edge-transitive cubic graphs of order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $2n$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math> is even and square-free. In particular, it is shown that such a graph is either symmetric or isomorphic to one of the following graphs: a semisymmetric graph of order 420, a semisymmetric graph of order 29,260, and five families of semisymmetric graphs constructed from the simple group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>PSL</mtext>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>p</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{bf{text{PSL}}}}_{2}(p)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"173-204"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263787","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
The maximum number of pentagons in a planar graph
一个平面图中五边形的最大数目
IF 0.9
3区 数学
Ervin Győri, Addisu Paulos, Nika Salia, Casey Tompkins, Oscar Zamora
{"title":"The maximum number of pentagons in a planar graph","authors":"Ervin Győri, Addisu Paulos, Nika Salia, Casey Tompkins, Oscar Zamora","doi":"10.1002/jgt.23172","DOIUrl":"https://doi.org/10.1002/jgt.23172","url":null,"abstract":"<p>In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math>-vertex planar graph. They precisely determined the maximum number of triangles and four-cycles and presented a conjecture for the maximum number of pentagons. In this work, we confirm their conjecture. Even more, we characterize the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math>-vertex, planar graphs with the maximum number of pentagons.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"229-256"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868691","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
Breaking small automorphisms by list colourings
通过列表着色打破小自变形
IF 0.9
3区 数学
Jakub Kwaśny, Marcin Stawiski
{"title":"Breaking small automorphisms by list colourings","authors":"Jakub Kwaśny, Marcin Stawiski","doi":"10.1002/jgt.23181","DOIUrl":"10.1002/jgt.23181","url":null,"abstract":"<p>For a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>, we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> that break every small automorphism of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. We show that such a colouring can be chosen from any set of lists of length 3. In addition, we show that any set of lists of length 2 on both edges and vertices of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> yields a total colouring which breaks all the small automorphisms of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. These results are sharp, and they match the known bounds for the nonlist variant.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 2","pages":"288-292"},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263792","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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