Journal of Graph Theory最新文献
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Universal graphs with forbidden wheel minors
具有禁止轮未成年人的通用图
IF 0.9
3区 数学
Thilo Krill
{"title":"Universal graphs with forbidden wheel minors","authors":"Thilo Krill","doi":"10.1002/jgt.23174","DOIUrl":"10.1002/jgt.23174","url":null,"abstract":"<p>Let <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow></math> be any wheel graph and <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> the class of all countable graphs not containing <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>W</mi>\u0000 </mrow></math> as a minor. We show that there exists a graph in <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> which contains every graph in <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> as an induced subgraph.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"100-112"},"PeriodicalIF":0.9,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199692","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 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
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":"<p>A graph is said to be <i>uniquely hamiltonian</i> 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 <span></span><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 <span></span><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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow></math> are outerplanar.</p>","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
Nonisomorphic two-dimensional algebraically defined graphs over R
R R 上的非同构二维代数定义图
IF 0.9
3区 数学
Brian G. Kronenthal, Joe Miller, Alex Nash, Jacob Roeder, Hani Samamah, Tony W. H. Wong
{"title":"Nonisomorphic two-dimensional algebraically defined graphs over \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23161:jgt23161-math-0001\" wiley:location=\"equation/jgt23161-math-0001.png\"><mrow><mrow><mi mathvariant=\"double-struck\">R</mi></mrow></mrow></math>","authors":"Brian G. Kronenthal, Joe Miller, Alex Nash, Jacob Roeder, Hani Samamah, Tony W. H. Wong","doi":"10.1002/jgt.23161","DOIUrl":"https://doi.org/10.1002/jgt.23161","url":null,"abstract":"<p>For <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 \u0000 <mo>:</mo>\u0000 \u0000 <msup>\u0000 <mi>R</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>→</mo>\u0000 \u0000 <mi>R</mi>\u0000 </mrow></math>, let <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 \u0000 <mi>R</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>f</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> be a two-dimensional algebraically defined graph, that is, a bipartite graph where each partite set is a copy of <span></span><math>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow></math> and two vertices <span></span><math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>a</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> and <span></span><math>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mrow>\u0000 <mi>x</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>x</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow></math> are adjacent if and only if <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>a</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <msub>\u0000 <mi>x</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msub>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>f</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>x</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"50-64"},"PeriodicalIF":0.9,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707817","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
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
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":"<p>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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> is a family of even subgraphs which cover all the edges of <span></span><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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> has an even subgraph cover with total length at most <span></span><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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow></math> satisfying the sufficient condition has a 4-even subgraph <span></span><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 <span></span><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 <span></span><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 <span></span><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
Dense circuit graphs and the planar Turán number of a cycle
密集电路图和循环的平面图兰数
IF 0.9
3区 数学
Ruilin Shi, Zach Walsh, Xingxing Yu
{"title":"Dense circuit graphs and the planar Turán number of a cycle","authors":"Ruilin Shi, Zach Walsh, Xingxing Yu","doi":"10.1002/jgt.23165","DOIUrl":"10.1002/jgt.23165","url":null,"abstract":"<p>The <i>planar Turán number</i> <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>ex</mtext>\u0000 \u0000 <mi>P</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>H</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> of a graph <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow></math> is the maximum number of edges in an <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-vertex planar graph without <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow></math> as a subgraph. Let <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow></math> denote the cycle of length <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>. The planar Turán number <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>ex</mtext>\u0000 \u0000 <mi>P</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow></math> is known for <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>7</mn>\u0000 </mrow></math>. We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large near triangulations, and we use this result to obtain consequences for planar Turán numbers. In particular, we prove that there is a constant <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow></math> so that <span></span><math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mtext>ex</mtext>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 1","pages":"27-38"},"PeriodicalIF":0.9,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23165","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943337","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
Strong arc decompositions of split digraphs
分裂图的强弧分解
IF 0.9
3区 数学
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":"<p>A <i>strong arc decomposition</i> of a digraph <span></span><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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow></math> into two sets <span></span><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 <span></span><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 <span></span><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 <span></span><math>\u0000 \u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow></math> such that every <span></span><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
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":"<p>A graph <span></span><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 <span></span><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 <span></span><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.</p>","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
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":"<p>We call a proper edge coloring of a graph <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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
{"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":"<p>A. Espuny Díaz, L. Lichev, D. Mitsche, and A. Wesolek, <i>Sharp threshold for embedding balanced spanning trees in random geometric graphs</i>, J. Graph Theory. <b>107</b> (2024), 107–125. https://doi.org/10.1002/jgt.23106</p><p>In 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.</p><p>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).”</p><p>The new Funding Information should read as follows:</p><p>Carl-Zeiss-Foundation.</p><p>Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), project no. 447645533.</p><p>Grant GrHyDy ANR-20-CE40-0002.</p><p>Fondecyt, Grant/Award Number: 1220174.</p><p>The Vanier Scholarship Program.</p><p>We apologize for this error.</p>","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
On the minimum number of arcs in 4-dicritical oriented graphs
论四临界定向图中的最小弧数
IF 0.9
3区 数学
Frédéric Havet, Lucas Picasarri-Arrieta, Clément Rambaud
{"title":"On the minimum number of arcs in 4-dicritical oriented graphs","authors":"Frédéric Havet, Lucas Picasarri-Arrieta, Clément Rambaud","doi":"10.1002/jgt.23159","DOIUrl":"10.1002/jgt.23159","url":null,"abstract":"<p>The dichromatic number <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mover>\u0000 <mi>χ</mi>\u0000 \u0000 <mo>→</mo>\u0000 </mover>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $overrightarrow{chi }(D)$</annotation>\u0000 </semantics></math> of a digraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> is the minimum number of colours needed to colour the vertices of a digraph such that each colour class induces an acyclic subdigraph. A digraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-dicritical if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mover>\u0000 <mi>χ</mi>\u0000 \u0000 <mo>→</mo>\u0000 </mover>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>D</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $overrightarrow{chi }(D)=k$</annotation>\u0000 </semantics></math> and each proper subdigraph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> satisfies <span></span><mat","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"107 4","pages":"778-809"},"PeriodicalIF":0.9,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866313","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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