Journal of Graph Theory最新文献

Hitting Times in the Binomial Random Graph 二项随机图中的命中次数

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-22 DOI: 10.1002/jgt.70057

Bertille Granet, Felix Joos, Jonathan Schrodt

{"title":"Hitting Times in the Binomial Random Graph","authors":"Bertille Granet, Felix Joos, Jonathan Schrodt","doi":"10.1002/jgt.70057","DOIUrl":"https://doi.org/10.1002/jgt.70057","url":null,"abstract":"Fix <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 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70057:jgt70057-math-0001\" wiley:location=\"equation/jgt70057-math-0001.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>2</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>, choose <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>log</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mfrac>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>p</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>Ω</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mi>log</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msup>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"377-393"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704516","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 a Clique-Building Game of Erdős 在一个集团建设游戏Erdős

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-14 DOI: 10.1002/jgt.70061

Alexandru Malekshahian, Sam Spiro

{"title":"On a Clique-Building Game of Erdős","authors":"Alexandru Malekshahian, Sam Spiro","doi":"10.1002/jgt.70061","DOIUrl":"https://doi.org/10.1002/jgt.70061","url":null,"abstract":"The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a <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 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0001\" wiley:location=\"equation/jgt70061-math-0001.png\"><mrow><mrow><msub><mi>K</mi><mi>n</mi></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at the end is strictly larger than the largest clique of their opponent; otherwise, Player 2 wins the game. Erdős conjectured that Player 2 always wins this game for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0002\" wiley:location=\"equation/jgt70061-math-0002.png\"><mrow><mrow><mi>n</mi><mo>unicode{x02265}</mo><mn>3</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. We make the first known progress on this problem, proving that this holds for at least 3/4 of all such <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0003\" wiley:location=\"equation/jgt70061-math-0003.png\"><mrow><mrow><mi>n</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>. We also address a biased version of this game, as well as the corresponding degree-building game, both of which were originally proposed by Erdős as well.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"208-221"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70061","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704252","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

Lower Bounds for Maximum Weight Bisections of Weighted Triangle-Free Subcubic Graphs 加权无三角次三次图的最大权等分下界

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-14 DOI: 10.1002/jgt.70056

Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou

{"title":"Lower Bounds for Maximum Weight Bisections of Weighted Triangle-Free Subcubic Graphs","authors":"Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou","doi":"10.1002/jgt.70056","DOIUrl":"https://doi.org/10.1002/jgt.70056","url":null,"abstract":"A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge-weighted triangle-free subcubic graphs and show that every weighted triangle-free subcubic graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>w</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70056:jgt70056-math-0001\" wiley:location=\"equation/jgt70056-math-0001.png\"><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>w</mi></mrow><mo>)</mo></mrow></mrow></math></annotation>\u0000 </semantics></math> has a bisection with weight at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>θ</mi>\u0000 \u0000 <mo>⋅</mo>\u0000 \u0000 <mi>w</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70056:jgt70056-math-0002\" wiley:location=\"equation/jgt70056-math-0002.png\"><mrow><mi>unicode{x003B8}</mi><mo>unicode{x022C5}</mo><mi>w</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></annotation>\u0000 </semantics></math> unless <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>≅</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"252-273"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Coarse Geometric Approach to Graph Layout Problems 图布局问题的粗糙几何方法

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-05 DOI: 10.1002/jgt.70058

Wanying Huang, David Hume, Samuel J. Kelly, Ryan Lam

{"title":"A Coarse Geometric Approach to Graph Layout Problems","authors":"Wanying Huang, David Hume, Samuel J. Kelly, Ryan Lam","doi":"10.1002/jgt.70058","DOIUrl":"https://doi.org/10.1002/jgt.70058","url":null,"abstract":"We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are monotonically nondecreasing with respect to a large-scale geometric generalisation of graph inclusion, and as such have potential applications in coarse geometry and geometric group theory. On the graph–theoretic side, we prove asymptotically optimal bounds on most of the above widths for the family of all finite subgraphs of any bounded degree graph whose separation profile is known to be of the form <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>r</mi>\u0000 \u0000 <mi>a</mi>\u0000 </msup>\u0000 \u0000 <mi>log</mi>\u0000 \u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>r</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mi>b</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math display=\"inline\" altimg=\"urn:x-wiley:03649024:media:jgt70058:jgt70058-math-0001\" xmlns=\"http://www.w3.org/1998/Math/MathML\" wiley:location=\"equation/jgt70058-math-0001.png\"><mrow><mrow><msup><mi>r</mi><mi>a</mi></msup><mi>log</mi><msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mi>b</mi></msup></mrow></mrow></math></annotation>\u0000 </semantics></math> for some <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math display=\"inline\" altimg=\"urn:x-wiley:03649024:media:jgt70058:jgt70058-math-0002\" xmlns=\"http://www.w3.org/1998/Math/MathML\" wiley:location=\"equation/jgt70058-math-0002.png\"><mrow><mrow><mi>a</mi><mo>unicode{x0003E}</mo><mn>0</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. This large class includes Diestel–Leader graphs, all Cayley graphs of nonvirtually cyclic polycyclic groups, uniform lattices in","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"169-194"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704458","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 Deep-Commuting Graph of Groups 关于群的深度可交换图

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-08 DOI: 10.1002/jgt.70059

Bahram Arvin, Behrouz Edalatzadeh, Ali Reza Salemkar

{"title":"On Deep-Commuting Graph of Groups","authors":"Bahram Arvin, Behrouz Edalatzadeh, Ali Reza Salemkar","doi":"10.1002/jgt.70059","DOIUrl":"https://doi.org/10.1002/jgt.70059","url":null,"abstract":"<div>\u0000 \u0000 The deep-commuting graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>DCom</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0001\" wiley:location=\"equation/jgt70059-math-0001.png\"><mrow><mrow><mtext>DCom</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> of a finite group <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0002\" wiley:location=\"equation/jgt70059-math-0002.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is the graph with vertex set <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0003\" wiley:location=\"equation/jgt70059-math-0003.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> such that two vertices <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0004\" wiley:location=\"equation/jgt70059-math-0004.png\"><mrow><mrow><mi>x</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0005\" wiley:location=\"equation/jgt70059-math-0005.png\"><mrow><mrow><mi>y</mi></mrow></mrow&gt","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"195-207"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704242","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

Bipartite Graphs With Minimum Degree at Least 15 Are Antimagic 最小度至少为15的二部图是反幻的

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-20 DOI: 10.1002/jgt.70069

Kecai Deng

{"title":"Bipartite Graphs With Minimum Degree at Least 15 Are Antimagic","authors":"Kecai Deng","doi":"10.1002/jgt.70069","DOIUrl":"https://doi.org/10.1002/jgt.70069","url":null,"abstract":"<div>\u0000 \u0000 An antimagic labeling of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \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 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70069:jgt70069-math-0001\" wiley:location=\"equation/jgt70069-math-0001.png\"><mrow><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> is a one-to-one mapping <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 \u0000 <mo>:</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>→</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70069:jgt70069-math-0002\" wiley:location=\"equation/jgt70069-math-0002.png\"><mrow><mrow><mi>f</mi><mo>:</mo><mi>E</mi><mo>unicode{x02192}</mo><mrow><mo class=\"MathClass-open\">{</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>unicode{x02026}</mo><mo>,</mo><mo>u","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"348-376"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704298","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 k

k

-Radius of 2-Connected Graphs 2连通图的k k半径

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-19 DOI: 10.1002/jgt.70065

Peter Dankelmann, Paul Horn

{"title":"The \u0000 \u0000 \u0000 k\u0000 \u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0001\" wiley:location=\"equation/jgt70065-math-0001.png\"><mrow><mi>k</mi></mrow></math>\u0000 -Radius of 2-Connected Graphs","authors":"Peter Dankelmann, Paul Horn","doi":"10.1002/jgt.70065","DOIUrl":"https://doi.org/10.1002/jgt.70065","url":null,"abstract":"<div>\u0000 \u0000 Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0002\" wiley:location=\"equation/jgt70065-math-0002.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math> be a connected graph. If <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0003\" wiley:location=\"equation/jgt70065-math-0003.png\"><mrow><mi>S</mi></mrow></math></annotation>\u0000 </semantics></math> is a set of vertices of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0004\" wiley:location=\"equation/jgt70065-math-0004.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0005\" wiley:location=\"equation/jgt70065-math-0005.png\"><mrow><mi>v</mi></mrow></math></annotation>\u0000 </semantics></math> is a vertex of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0006\" wiley:location=\"equation/jgt70065-math-0006.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math>, then the distance <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>S</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0007\" wiley:location","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"286-310"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704300","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

Realizing Degree Sequences With S 3

S_{3}

-Connected Graphs 用S3连通图实现度序列

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-14 DOI: 10.1002/jgt.70062

Rui Guan, Chenglin Jiang, Hong-Jian Lai, Jiaao Li, Xinyuan Li

{"title":"Realizing Degree Sequences With \u0000 \u0000 \u0000 \u0000 \u0000 S\u0000 3\u0000 \u0000 \u0000 \u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0001\" wiley:location=\"equation/jgt70062-math-0001.png\"><mrow><mrow><msub><mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">S</mi><mn>3</mn></msub></mrow></mrow></math>\u0000 -Connected Graphs","authors":"Rui Guan, Chenglin Jiang, Hong-Jian Lai, Jiaao Li, Xinyuan Li","doi":"10.1002/jgt.70062","DOIUrl":"https://doi.org/10.1002/jgt.70062","url":null,"abstract":"<div>\u0000 \u0000 A graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0002\" wiley:location=\"equation/jgt70062-math-0002.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>S</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0003\" wiley:location=\"equation/jgt70062-math-0003.png\"><mrow><mrow><msub><mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">S</mi><mn>3</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math>-connected if, for any mapping <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>β</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 \u0000 <mo>↦</mo>\u0000 \u0000 <msub>\u0000 <mi>Z</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0004\" wiley:location=\"equation/jgt70062-math-0004.png\"><mrow><mrow><mi>unicode{x003B2}</mi><mo>:</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>unicode{x021A6}</mo><msub><mi mathvariant=\"double-struck\">Z</mi><mn>3</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mo>∑</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"222-236"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704254","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 the Hardness of Switching to a Small Number of Edges 关于切换到少量边的硬度

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-14 DOI: 10.1002/jgt.70063

Vít Jelínek, Eva Jelínková, Jan Kratochvíl

引用次数: 0

Normal Approximation for Subgraph Count in Random Hypergraphs 随机超图中子图计数的正态逼近

IF 1 3区数学

Journal of Graph Theory Pub Date : 2026-08-11 Epub Date: 2026-05-19 DOI: 10.1002/jgt.70066

Mikołaj Nieradko, Wojciech Michalczuk, Grzegorz Serafin

{"title":"Normal Approximation for Subgraph Count in Random Hypergraphs","authors":"Mikołaj Nieradko, Wojciech Michalczuk, Grzegorz Serafin","doi":"10.1002/jgt.70066","DOIUrl":"https://doi.org/10.1002/jgt.70066","url":null,"abstract":"<div>\u0000 \u0000 A nonuniform and inhomogeneous random hypergraph model is considered, which is a straightforward extension of the celebrated binomial random graph model <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>p</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70066:jgt70066-math-0001\" wiley:location=\"equation/jgt70066-math-0001.png\"><mrow><mrow><mi mathvariant=\"double-struck\">G</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>,</mo><mi>p</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math>. We establish necessary and sufficient conditions for the small hypergraph count to be asymptotically normal, and complement them with convergence rates in both the Wasserstein and Kolmogorov distances. Next we narrow our attention to the homogeneous model and relate the obtained results to the fourth moment phenomenon. Additionally, a short proof of the necessity of the aforementioned conditions is presented, which seems to be absent in the literature, even in the context of the model <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>p</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70066:jgt70066-math-0002\" wiley:location=\"equation/jgt70066-math-0002.png\"><mrow><mrow><mi mathvariant=\"double-struck\">G</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>,</mo><mi>p</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math>.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"311-347"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704301","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