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Induced Subgraphs of Induced Subgraphs of Large Chromatic Number 大色数诱导子图的诱导子图
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-09-25 DOI: 10.1007/s00493-023-00061-4
António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Alex Scott, Youri Tamitegama, Jane Tan
{"title":"Induced Subgraphs of Induced Subgraphs of Large Chromatic Number","authors":"António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Alex Scott, Youri Tamitegama, Jane Tan","doi":"10.1007/s00493-023-00061-4","DOIUrl":"https://doi.org/10.1007/s00493-023-00061-4","url":null,"abstract":"<p>We prove that, for every graph <i>F</i> with at least one edge, there is a constant <span>(c_F)</span> such that there are graphs of arbitrarily large chromatic number and the same clique number as <i>F</i> in which every <i>F</i>-free induced subgraph has chromatic number at most <span>(c_F)</span>. This generalises recent theorems of Briański, Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Our results imply that for every <span>(rgeqslant 3)</span> the class of <span>(K_r)</span>-free graphs has a very strong vertex Ramsey-type property, giving a vast generalisation of a result of Folkman from 1970. We also prove related results for tournaments, hypergraphs and infinite families of graphs, and show an analogous statement for graphs where clique number is replaced by odd girth.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"12 13","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
Integer Multiflows in Acyclic Planar Digraphs 非循环平面有向图中的整数多流
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-09-19 DOI: 10.1007/s00493-023-00065-0
Guyslain Naves
{"title":"Integer Multiflows in Acyclic Planar Digraphs","authors":"Guyslain Naves","doi":"10.1007/s00493-023-00065-0","DOIUrl":"https://doi.org/10.1007/s00493-023-00065-0","url":null,"abstract":"<p>We give an algorithm with complexity <span>(O((R+1)^{4k^2} k^3 n))</span> for the integer multiflow problem on instances (<i>G</i>, <i>H</i>, <i>r</i>, <i>c</i>) with <i>G</i> an acyclic planar digraph and <span>(r+c)</span> Eulerian. Here, <span>(n = |V(G)|)</span>, <span>(k = |E(H)|)</span> and <i>R</i> is the maximum request <span>(max _{h in E(H)} r(h))</span>. When <i>k</i> is fixed, this gives a polynomial-time algorithm for the arc-disjoint paths problem under the same hypothesis.Kindly check and confirm the edit made in the title.Confirmed\u0000Journal instruction requires a city and country for affiliations; however, these are missing in affiliation [1]. Please verify if the provided city is correct and amend if necessary.Since the submission, my affiliation has changed. It should now be:\u0000Laboratoire d'Informatique &amp; Systèmes, Aix-Marseille Université, CNRS UMR 7020, Marseille, France</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Effective Results on the Size and Structure of Sumsets Sumset大小和结构的有效结果
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-09-18 DOI: 10.1007/s00493-023-00055-2
Andrew Granville, George Shakan, Aled Walker
{"title":"Effective Results on the Size and Structure of Sumsets","authors":"Andrew Granville, George Shakan, Aled Walker","doi":"10.1007/s00493-023-00055-2","DOIUrl":"https://doi.org/10.1007/s00493-023-00055-2","url":null,"abstract":"<p>Let <span>(A subset {mathbb {Z}}^d)</span> be a finite set. It is known that <i>NA</i> has a particular size (<span>(vert NAvert = P_A(N))</span> for some <span>(P_A(X) in {mathbb {Q}}[X])</span>) and structure (all of the lattice points in a cone other than certain exceptional sets), once <i>N</i> is larger than some threshold. In this article we give the first effective upper bounds for this threshold for arbitrary <i>A</i>. Such explicit results were only previously known in the special cases when <span>(d=1)</span>, when the convex hull of <i>A</i> is a simplex or when <span>(vert Avert = d+2)</span> Curran and Goldmakher (Discrete Anal. Paper No. 27, 2021), results which we improve.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 3
Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path 色数的多项式界。IV： 排除五顶点路径的一个近多项式界
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-09-15 DOI: 10.1007/s00493-023-00015-w
Alex Scott, Paul Seymour, Sophie Spirkl
{"title":"Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path","authors":"Alex Scott, Paul Seymour, Sophie Spirkl","doi":"10.1007/s00493-023-00015-w","DOIUrl":"https://doi.org/10.1007/s00493-023-00015-w","url":null,"abstract":"<p>A graph <i>G</i> is <i>H</i><i>-free</i> if it has no induced subgraph isomorphic to <i>H</i>. We prove that a <span>(P_5)</span>-free graph with clique number <span>(omega ge 3)</span> has chromatic number at most <span>(omega ^{log _2(omega )})</span>. The best previous result was an exponential upper bound <span>((5/27)3^{omega })</span>, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erdős-Hajnal conjecture holds for <span>(P_5)</span>, which is the smallest open case. Thus, there is great interest in whether there is a polynomial bound for <span>(P_5)</span>-free graphs, and our result is an attempt to approach that.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 2","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 18
Separating Polynomial $$chi $$ -Boundedness from $$chi $$ -Boundedness 从$$chi$$-有界性分离多项式$$chi$$-有界
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-08-09 DOI: 10.1007/s00493-023-00054-3
Marcin Briański, James Davies, Bartosz Walczak
{"title":"Separating Polynomial $$chi $$ -Boundedness from $$chi $$ -Boundedness","authors":"Marcin Briański, James Davies, Bartosz Walczak","doi":"10.1007/s00493-023-00054-3","DOIUrl":"https://doi.org/10.1007/s00493-023-00054-3","url":null,"abstract":"<p>Extending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function <span>(f:mathbb {N}rightarrow mathbb {N}cup {infty })</span> with <span>(f(1)=1)</span> and <span>(f(n)geqslant left( {begin{array}{c}3n+1 3end{array}}right) )</span>, we construct a hereditary class of graphs <span>({mathcal {G}})</span> such that the maximum chromatic number of a graph in <span>({mathcal {G}})</span> with clique number <i>n</i> is equal to <i>f</i>(<i>n</i>) for every <span>(nin mathbb {N})</span>. In particular, we prove that there exist hereditary classes of graphs that are <span>(chi )</span>-bounded but not polynomially <span>(chi )</span>-bounded.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"13 23","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 18
Γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Gamma $$end{document}-Graphic Delta-Matroids and Their Applications Γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Gamma $$end{document}-Graphic Delta-Matroids and Their Applications
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-06-13 DOI: 10.1007/s00493-023-00043-6
Donggyu Kim, Duksang Lee, Sang-il Oum
{"title":"Γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Gamma $$end{document}-Graphic Delta-Matroids and Their Applications","authors":"Donggyu Kim, Duksang Lee, Sang-il Oum","doi":"10.1007/s00493-023-00043-6","DOIUrl":"https://doi.org/10.1007/s00493-023-00043-6","url":null,"abstract":"","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"43 1","pages":"963 - 983"},"PeriodicalIF":1.1,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46661245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Enclosing Depth and Other Depth Measures 围护深度和其他深度测量
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-06-13 DOI: 10.1007/s00493-023-00045-4
Patrick Schnider
{"title":"Enclosing Depth and Other Depth Measures","authors":"Patrick Schnider","doi":"10.1007/s00493-023-00045-4","DOIUrl":"https://doi.org/10.1007/s00493-023-00045-4","url":null,"abstract":"<p>We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the <i>Cascade conjecture</i>, introduced by Kalai for Tverberg depth, holds for all depth measures which satisfy our most restrictive set of axioms, which includes Tukey depth. Along the way, we introduce and study a new depth measure called <i>enclosing depth</i>, which we believe to be of independent interest, and show its relation to a constant-fraction Radon theorem on certain two-colored point sets.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"14 12","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71493259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1
The Chromatic Number of the Product of 5-Chromatic Graphs can be 4 五色图积的色数可为4
2区 数学
Combinatorica Pub Date : 2023-06-12 DOI: 10.1007/s00493-023-00047-2
Claude Tardif
{"title":"The Chromatic Number of the Product of 5-Chromatic Graphs can be 4","authors":"Claude Tardif","doi":"10.1007/s00493-023-00047-2","DOIUrl":"https://doi.org/10.1007/s00493-023-00047-2","url":null,"abstract":"","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136309718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 7
A Local Version of Katona’s Intersecting Shadow Theorem Katona相交阴影定理的局部版本
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-06-05 DOI: 10.1007/s00493-023-00048-1
M. Sales, B. Schülke
{"title":"A Local Version of Katona’s Intersecting Shadow Theorem","authors":"M. Sales, B. Schülke","doi":"10.1007/s00493-023-00048-1","DOIUrl":"https://doi.org/10.1007/s00493-023-00048-1","url":null,"abstract":"","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43389802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Counting Hamilton Cycles in Dirac Hypergraphs 狄拉克超图中Hamilton环的计数
IF 1.1 2区 数学
Combinatorica Pub Date : 2023-05-23 DOI: 10.1007/s00493-023-00029-4
Asaf Ferber, Liam Hardiman, Adva Mond
{"title":"Counting Hamilton Cycles in Dirac Hypergraphs","authors":"Asaf Ferber, Liam Hardiman, Adva Mond","doi":"10.1007/s00493-023-00029-4","DOIUrl":"https://doi.org/10.1007/s00493-023-00029-4","url":null,"abstract":"","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"43 1","pages":"665 - 680"},"PeriodicalIF":1.1,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42392798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1
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