Journal of Graph Theory最新文献_第8页

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

Journal of Graph Theory Pub Date : 2024-09-16 DOI: 10.1002/jgt.23179

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":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a simple graph and let <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 <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 <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 <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 <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

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

Journal of Graph Theory Pub Date : 2024-09-16 DOI: 10.1002/jgt.23181

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":"For a graph <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 <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> that break every small automorphism of <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 <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 <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.","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}

引用次数: 0

Variants of the Gyárfás–Sumner conjecture: Oriented trees and rainbow paths Gyárfás-Sumner 猜想的变体：定向树和彩虹路径

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-09-10 DOI: 10.1002/jgt.23171

Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis, Karthik Murali

{"title":"Variants of the Gyárfás–Sumner conjecture: Oriented trees and rainbow paths","authors":"Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis, Karthik Murali","doi":"10.1002/jgt.23171","DOIUrl":"10.1002/jgt.23171","url":null,"abstract":"Given a finite family <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math> of graphs, we say that a graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is “<math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math>-free” if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> does not contain any graph in <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math> as a subgraph. We abbreviate <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math>-free to just “<math>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow></math>-free” when <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mi>F</mi>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow></math>. A vertex-colored graph <math>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow></math> is called “rainbow” if no two vertices of <math>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow></math> have the same color. Given an integer <math>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 </mrow></math> and a finite family of graphs <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math>, let <math>\u0000 \u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>ℱ</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> denote the smallest integer such that any properly vertex-colored <math>\u0000 \u0000 <mrow>\u0000 <mi>ℱ</mi>\u0000 </mrow></math>-free graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> having <math>\u0000 \u0000 <mrow>\u0000 <mi>χ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mi>ℓ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"136-161"},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199689","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

Removable edges in near-bipartite bricks 近似二方砖中的可移动边缘

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-09-09 DOI: 10.1002/jgt.23173

Yipei Zhang, Fuliang Lu, Xiumei Wang, Jinjiang Yuan

{"title":"Removable edges in near-bipartite bricks","authors":"Yipei Zhang, Fuliang Lu, Xiumei Wang, Jinjiang Yuan","doi":"10.1002/jgt.23173","DOIUrl":"10.1002/jgt.23173","url":null,"abstract":"An edge <math>\u0000 \u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow></math> of a matching covered graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is removable if <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>e</mi>\u0000 </mrow></math> is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching covered graphs introduced by Lovász and Plummer. A nonbipartite matching covered graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is a brick if it is free of nontrivial tight cuts. Carvalho, Lucchesi and Murty proved that every brick other than <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msub>\u0000 </mrow></math> and <math>\u0000 \u0000 <mrow>\u0000 <mover>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mn>6</mn>\u0000 </msub>\u0000 \u0000 <mo>¯</mo>\u0000 </mover>\u0000 </mrow></math> has at least <math>\u0000 \u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math> removable edges. A brick <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is near-bipartite if it has a pair of edges <math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow></math> such that <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>e</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"113-135"},"PeriodicalIF":0.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199691","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 vertex-transitive graphs with a unique hamiltonian cycle 关于具有唯一哈密顿循环的顶点变换图

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-08-22 DOI: 10.1002/jgt.23166

Babak Miraftab, Dave Witte Morris

{"title":"On vertex-transitive graphs with a unique hamiltonian cycle","authors":"Babak Miraftab, Dave Witte Morris","doi":"10.1002/jgt.23166","DOIUrl":"10.1002/jgt.23166","url":null,"abstract":"A graph is said to be uniquely hamiltonian if it has a unique hamiltonian cycle. For a natural extension of this concept to infinite graphs, we find all uniquely hamiltonian vertex-transitive graphs with finitely many ends, and also discuss some examples with infinitely many ends. In particular, we show each nonabelian free group <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow></math> has a Cayley graph of degree <math>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math> that has a unique hamiltonian circle. (A weaker statement had been conjectured by Georgakopoulos.) Furthermore, we prove that these Cayley graphs of <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow></math> are outerplanar.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"65-99"},"PeriodicalIF":0.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23166","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199693","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

Five-cycle double cover and shortest cycle cover 五周期双覆盖和最短周期覆盖

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-08-11 DOI: 10.1002/jgt.23164

Siyan Liu, Rong-Xia Hao, Rong Luo, Cun-Quan Zhang

{"title":"Five-cycle double cover and shortest cycle cover","authors":"Siyan Liu, Rong-Xia Hao, Rong Luo, Cun-Quan Zhang","doi":"10.1002/jgt.23164","DOIUrl":"10.1002/jgt.23164","url":null,"abstract":"The 5-even subgraph cycle double cover conjecture (5-CDC conjecture) asserts that every bridgeless graph has a 5-even subgraph double cover. A shortest even subgraph cover of a graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is a family of even subgraphs which cover all the edges of <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> and the sum of their lengths is minimum. It is conjectured that every bridgeless graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> has an even subgraph cover with total length at most <math>\u0000 \u0000 <mrow>\u0000 <mfrac>\u0000 <mn>21</mn>\u0000 \u0000 <mn>15</mn>\u0000 </mfrac>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow></math>. In this paper, we study those two conjectures for weak oddness 2 cubic graphs and present a sufficient condition for such graphs to have a 5-CDC containing a member with many vertices. As a corollary, we show that for every oddness 2 cubic graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> satisfying the sufficient condition has a 4-even subgraph <math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math>-cover with total length at most <math>\u0000 \u0000 <mrow>\u0000 <mfrac>\u0000 <mn>20</mn>\u0000 \u0000 <mn>15</mn>\u0000 </mfrac>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math>. We also show that every oddness 2 cubic graph <math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> with girth at least 30 has a 5-CDC containing a member of length at least <math>\u0000 \u0000 <mrow>\u0000 <mfrac>\u0000 <mn>9</mn>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"39-49"},"PeriodicalIF":0.9,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943300","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

Strong arc decompositions of split digraphs 分裂图的强弧分解

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-08-06 DOI: 10.1002/jgt.23157

Jørgen Bang-Jensen, Yun Wang

{"title":"Strong arc decompositions of split digraphs","authors":"Jørgen Bang-Jensen, Yun Wang","doi":"10.1002/jgt.23157","DOIUrl":"10.1002/jgt.23157","url":null,"abstract":"A strong arc decomposition of a digraph <math>\u0000 \u0000 <mrow>\u0000 <mi>D</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>A</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> is a partition of its arc set <math>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow></math> into two sets <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>A</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>A</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow></math> such that the digraph <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>D</mi>\u0000 \u0000 <mi>i</mi>\u0000 </msub>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>A</mi>\u0000 \u0000 <mi>i</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> is strong for <math>\u0000 \u0000 <mrow>\u0000 <mi>i</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math>. Bang-Jensen and Yeo conjectured that there is some <math>\u0000 \u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow></math> such that every <math>\u0000 \u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow></math>-arc-strong digraph has a strong arc decomposition. They also proved that with one exception on four vertices every 2-arc-strong semicomplete digraph has a strong arc decomposition. Bang-Jensen and Huang extended this result to locally semicomplete digraphs by proving that every 2-arc-strong locally semicomplete digraph which is not the square of an even cycle h","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"5-26"},"PeriodicalIF":0.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23157","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943301","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

Stability of Rose Window graphs 玫瑰窗图形的稳定性

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-08-05 DOI: 10.1002/jgt.23162

Milad Ahanjideh, István Kovács, Klavdija Kutnar

{"title":"Stability of Rose Window graphs","authors":"Milad Ahanjideh, István Kovács, Klavdija Kutnar","doi":"10.1002/jgt.23162","DOIUrl":"10.1002/jgt.23162","url":null,"abstract":"A graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{Gamma }}$</annotation>\u0000 </semantics></math> is said to be stable if for the direct product <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mtext>Aut</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>Γ</mi>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{Gamma }}times {{bf{K}}}_{2},text{Aut}({rm{Gamma }}times {{bf{K}}}_{2})$</annotation>\u0000 </semantics></math> is isomorphic to <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>Aut</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>Γ</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>×</mo>\u0000 \u0000 <msub>\u0000 <mi>Z</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $text{Aut}({rm{Gamma }})times {{mathbb{Z}}}_{2}$</annotation>\u0000 </semantics></math>; otherwise, it is called unstable. An unstable graph is called nontrivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all nontrivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"107 4","pages":"810-832"},"PeriodicalIF":0.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943338","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

Proper edge colorings of planar graphs with rainbow C 4 ${C}_{4}$ -s 具有彩虹 C4 ${C}_{4}$-s 的平面图的适当边着色

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-08-05 DOI: 10.1002/jgt.23163

András Gyárfás, Ryan R. Martin, Miklós Ruszinkó, Gábor N. Sárközy

{"title":"Proper edge colorings of planar graphs with rainbow \u0000 \u0000 \u0000 \u0000 \u0000 C\u0000 4\u0000 \u0000 \u0000 \u0000 ${C}_{4}$\u0000 -s","authors":"András Gyárfás, Ryan R. Martin, Miklós Ruszinkó, Gábor N. Sárközy","doi":"10.1002/jgt.23163","DOIUrl":"10.1002/jgt.23163","url":null,"abstract":"We call a proper edge coloring of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> a B-coloring if every 4-cycle of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is colored with four different colors. Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>q</mi>\u0000 \u0000 <mi>B</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${q}_{B}(G)$</annotation>\u0000 </semantics></math> denote the smallest number of colors needed for a B-coloring of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. Motivated by earlier papers on B-colorings, here we consider <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>q</mi>\u0000 \u0000 <mi>B</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${q}_{B}(G)$</annotation>\u0000 </semantics></math> for planar and outerplanar graphs in terms of the maximum degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>Δ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${rm{Delta }}={rm{Delta }}(G)$</annotation>\u0000 </sem","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"107 4","pages":"833-846"},"PeriodicalIF":0.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943351","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

Correction to “Sharp threshold for embedding balanced spanning trees in random geometric graphs” 对 "在随机几何图中嵌入平衡生成树的锐阈值 "的更正

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-07-31 DOI: 10.1002/jgt.23160

{"title":"Correction to “Sharp threshold for embedding balanced spanning trees in random geometric graphs”","authors":"","doi":"10.1002/jgt.23160","DOIUrl":"10.1002/jgt.23160","url":null,"abstract":"A. Espuny Díaz, L. Lichev, D. Mitsche, and A. Wesolek, Sharp threshold for embedding balanced spanning trees in random geometric graphs, J. Graph Theory. 107 (2024), 107–125. https://doi.org/10.1002/jgt.23106In the “ACKNOWLEDGMENTS” section, the text “The research leading to these results has been supported by the Carl-Zeiss-Foundation (Alberto Espuny Díaz), by grant GrHyDy ANR-20-CE40-0002, and by Fondecyt grant 1220174 (Dieter Mitsche) and by the Vanier Scholarship Program (Alexandra Wesolek).” was incorrect.This should have read: “The research leading to these results has been supported by the Carl-Zeiss-Foundation and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through project no. 447645533 (A. Espuny Díaz), by grant GrHyDy ANR-20-CE40-0002 and by Fondecyt grant 1220174 (D. Mitsche) and by the Vanier Scholarship Program (A. Wesolek).”The new Funding Information should read as follows:Carl-Zeiss-Foundation.Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project no. 447645533.Grant GrHyDy ANR-20-CE40-0002.Fondecyt, Grant/Award Number: 1220174.The Vanier Scholarship Program.We apologize for this error.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"107 4","pages":"847"},"PeriodicalIF":0.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23160","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866312","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