Journal of Graph Theory最新文献

Equitable List Coloring of Planar Graphs With Given Maximum Degree

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-15 DOI: 10.1002/jgt.23203

H. A. Kierstead, Alexandr Kostochka, Zimu Xiang

{"title":"Equitable List Coloring of Planar Graphs With Given Maximum Degree","authors":"H. A. Kierstead, Alexandr Kostochka, Zimu Xiang","doi":"10.1002/jgt.23203","DOIUrl":"https://doi.org/10.1002/jgt.23203","url":null,"abstract":"If <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation> $L$</annotation>\u0000 </semantics></math> is a list assignment of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation> $r$</annotation>\u0000 </semantics></math> colors to each vertex of an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math>-vertex graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>, then an equitable <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation> $L$</annotation>\u0000 </semantics></math>-coloring of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a proper coloring of vertices of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> from their lists such that no color is used more than <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⌈</mo>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>/</mo>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <mo>⌉</mo>\u0000 </mrow>\u0000 <annotation> $lceil n/rrceil $</annotation>\u0000 </semantics></math> times. A graph is equitably <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation> $r$</annotation>\u0000 </semantics></math>-choosable if it has an equitable <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation> $L$</annotation>\u0000 </semantics></math>-coloring for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation> $r$</annotation>\u0000 </semantics></math>-list assignment <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"832-838"},"PeriodicalIF":0.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23203","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143456080","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 Pre- and Post-Positional Semi-Random Graph Processes 关于前置和后置半随机图过程

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-12 DOI: 10.1002/jgt.23202

Pu Gao, Hidde Koerts

{"title":"On the Pre- and Post-Positional Semi-Random Graph Processes","authors":"Pu Gao, Hidde Koerts","doi":"10.1002/jgt.23202","DOIUrl":"https://doi.org/10.1002/jgt.23202","url":null,"abstract":"We study the semi-random graph process, and a variant process recently suggested by Nick Wormald. We show that these two processes are asymptotically equally fast in constructing a semi-random graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> that has property <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{P}}$</annotation>\u0000 </semantics></math>, for the following examples of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{P}}$</annotation>\u0000 </semantics></math>: (1) <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{P}}$</annotation>\u0000 </semantics></math> is the set of graphs containing a fixed <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation> $d$</annotation>\u0000 </semantics></math>-degenerate subgraph, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation> $dge 1$</annotation>\u0000 </semantics></math> is fixed and (2) <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{P}}$</annotation>\u0000 </semantics></math> is the set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-connected graphs, where <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation> $kge 1$</annotation>\u0000 </semantics></math> is fixed. In particular, our result of the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-connectedness above settles the open case <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"819-831"},"PeriodicalIF":0.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23202","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455949","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 Question of Erdős and Nešetřil About Minimal Cuts in a Graph

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-08 DOI: 10.1002/jgt.23207

Domagoj Bradač

引用次数: 0

Hypergraph Anti-Ramsey Theorems

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-08 DOI: 10.1002/jgt.23204

Xizhi Liu, Jialei Song

{"title":"Hypergraph Anti-Ramsey Theorems","authors":"Xizhi Liu, Jialei Song","doi":"10.1002/jgt.23204","DOIUrl":"https://doi.org/10.1002/jgt.23204","url":null,"abstract":"<div>\u0000 \u0000 The anti-Ramsey number <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mtext>ar</mtext>\u0000 \u0000 <mrow>\u0000 \u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>F</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>\u0000 $text{ar}(n,F)$\u0000</annotation>\u0000 </semantics>\u0000 </math> of an <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $r$\u0000</annotation>\u0000 </semantics>\u0000 </math>-graph <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $F$\u0000</annotation>\u0000 </semantics>\u0000 </math> is the minimum number of colors needed to color the complete <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $n$\u0000</annotation>\u0000 </semantics>\u0000 </math>-vertex <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $r$\u0000</annotation>\u0000 </semantics>\u0000 </math>-graph to ensure the existence of a rainbow copy of <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $F$\u0000</annotation>\u0000 </semantics>\u0000 </math>. We establish a removal-type result for the anti-Ramsey problem of <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $F$\u0000</annotation>\u0000 </semantics>\u0000 </math> when <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>\u0000 $F$\u0000</annotation>\u0000 </semantics>\u0000 </math> is the expansion of a hypergraph with a smaller uniformity. We present two applications of this result. First, we refine the general bound <math>\u0000 \u0000 <semantics>\u0000 \u0000 <mrow>\u0000 <mtext>ar</mtext>\u0000 \u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"808-816"},"PeriodicalIF":0.9,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455744","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

Small Planar Hypohamiltonian Graphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-12-04 DOI: 10.1002/jgt.23205

Cheng-Chen Tsai

{"title":"Small Planar Hypohamiltonian Graphs","authors":"Cheng-Chen Tsai","doi":"10.1002/jgt.23205","DOIUrl":"https://doi.org/10.1002/jgt.23205","url":null,"abstract":"<div>\u0000 \u0000 A graph is hypohamiltonian if it is non-hamiltonian, but the deletion of every single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 40 vertices, a result due to Jooyandeh, McKay, Östergård, Pettersson, and Zamfirescu. That result is here improved upon by two planar hypohamiltonian graphs on 34 vertices. We exploited a special subgraph contained in two graphs of Jooyandeh et al., and modified it to construct the two 34-vertex graphs and six planar hypohamiltonian graphs on 37 vertices. Each of the 34-vertex graphs has 26 cubic vertices, improving upon the result of Jooyandeh et al. that planar hypohamiltonian graphs have 30 cubic vertices. We use the 34-vertex graphs to construct hypohamiltonian graphs of order 34 with crossing number 1, improving the best-known bound of 36 due to Wiener. Whether there exists a planar hypohamiltonian graph on 41 vertices was an open question. We settled this question by applying an operation introduced by Thomassen to the 37-vertex graphs to obtain several planar hypohamiltonian graphs on 41 vertices. The 25 planar hypohamiltonian graphs on 40 vertices of Jooyandeh et al. have no nontrivial automorphisms. The result is here improved upon by six planar hypohamiltonian graphs on 40 vertices with nontrivial automorphisms.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"799-807"},"PeriodicalIF":0.9,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455664","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

Tight Upper Bound on the Clique Size in the Square of 2-Degenerate Graphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-11-27 DOI: 10.1002/jgt.23201

Seog-Jin Kim, Xiaopan Lian

{"title":"Tight Upper Bound on the Clique Size in the Square of 2-Degenerate Graphs","authors":"Seog-Jin Kim, Xiaopan Lian","doi":"10.1002/jgt.23201","DOIUrl":"https://doi.org/10.1002/jgt.23201","url":null,"abstract":"<div>\u0000 \u0000 The square of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>, denoted <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation> ${G}^{2}$</annotation>\u0000 </semantics></math>, has the same vertex set as <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> and has an edge between two vertices if the distance between them in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is at most 2. In general, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>χ</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <msup>\u0000 <mi>G</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>Δ</mi>\u0000 \u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation> ${rm{Delta }}(G)+1le chi ({G}^{2})le {rm{Delta }}{(G)}^{2}+1$</annotation>\u0000 </semantics></math> for every graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. Charpentier (2014) asked whether <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <m","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"781-798"},"PeriodicalIF":0.9,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455925","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 odd cycles in a planar graph

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-11-10 DOI: 10.1002/jgt.23197

Emily Heath, Ryan R. Martin, Chris Wells

{"title":"The maximum number of odd cycles in a planar graph","authors":"Emily Heath, Ryan R. Martin, Chris Wells","doi":"10.1002/jgt.23197","DOIUrl":"https://doi.org/10.1002/jgt.23197","url":null,"abstract":"How many copies of a fixed odd cycle, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>m</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${C}_{2m+1}$</annotation>\u0000 </semantics></math>, can a planar graph contain? We answer this question asymptotically for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>∈</mo>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $min {2,3,4}$</annotation>\u0000 </semantics></math> and prove a bound which is tight up to a factor of 3/2 for all other values of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math>. This extends the prior results of Cox and Martin and of Lv, Győri, He, Salia, Tompkins, and Zhu on the analogous question for even cycles. Our bounds result from a reduction to the following maximum likelihood question: which probability mass <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation> $mu $</annotation>\u0000 </semantics></math> on the edges of some clique maximizes the probability that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math> edges sampled independently from <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation> $mu $</annotation>\u0000 </semantics></math> form either a cycle or a path?","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"745-780"},"PeriodicalIF":0.9,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23197","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143456010","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

Odd chromatic number of graph classes

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-11-06 DOI: 10.1002/jgt.23200

Rémy Belmonte, Ararat Harutyunyan, Noleen Köhler, Nikolaos Melissinos

{"title":"Odd chromatic number of graph classes","authors":"Rémy Belmonte, Ararat Harutyunyan, Noleen Köhler, Nikolaos Melissinos","doi":"10.1002/jgt.23200","DOIUrl":"https://doi.org/10.1002/jgt.23200","url":null,"abstract":"A graph is called odd (respectively, even) if every vertex has odd (respectively, even) degree. Gallai proved that every graph can be partitioned into two even induced subgraphs, or into an odd and an even induced subgraph. We refer to a partition into odd subgraphs as an odd colouring of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. Scott proved that a connected graph admits an odd colouring if and only if it has an even number of vertices. We say that a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-odd colourable if it can be partitioned into at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math> odd induced subgraphs. The odd chromatic number of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>, denoted by <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 \u0000 <mtext>odd</mtext>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${chi }_{text{odd}}(G)$</annotation>\u0000 </semantics></math>, is the minimum integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math> for which <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-odd colourable. We initiate the systematic study of odd colouring and odd chromatic number of graph classes. We fir","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"722-744"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23200","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455839","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

The effect of symmetry-preserving operations on 3-connectivity

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-11-04 DOI: 10.1002/jgt.23196

Heidi Van den Camp

引用次数: 0

Edge-arc-disjoint paths in semicomplete mixed graphs

IF 0.9 3区数学

Journal of Graph Theory Pub Date : 2024-11-04 DOI: 10.1002/jgt.23199

J. Bang-Jensen, Y. Wang

{"title":"Edge-arc-disjoint paths in semicomplete mixed graphs","authors":"J. Bang-Jensen, Y. Wang","doi":"10.1002/jgt.23199","DOIUrl":"https://doi.org/10.1002/jgt.23199","url":null,"abstract":"The so-called weak-2-linkage problem asks for a given digraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>,</mo>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $D=(V,A)$</annotation>\u0000 </semantics></math> and distinct vertices <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>s</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>t</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>t</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${s}_{1},{s}_{2},{t}_{1},{t}_{2}$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> whether <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation> $D$</annotation>\u0000 </semantics></math> has arc-disjoint paths <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${P}_{1},{P}_{2}$</annotation>\u0000 </semantics></math> so that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${P}_{i}$</annotation>\u0000 </semantics></math> is an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <msub>\u0000 <mi>s</mi>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"705-721"},"PeriodicalIF":0.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455667","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