{"title":"色度数大的高连接子图","authors":"Tung H. Nguyen","doi":"10.1137/22m150040x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 243-260, March 2024. <br/> Abstract. For integers [math] and [math], let [math] be the least integer [math] such that every graph with chromatic number at least [math] contains a [math]-connected subgraph with chromatic number at least [math]. Refining the recent result of Girão and Narayanan [Bull. Lond. Math. Soc., 54 (2022), pp. 868–875] that [math] for all [math], we prove that [math] for all [math] and [math]. This sharpens earlier results of Alon et al. [J. Graph Theory, 11 (1987), pp. 367–371], of Chudnovsky [J. Combin. Theory Ser. B, 103 (2013), pp. 567–586], and of Penev, Thomassé, and Trotignon [SIAM J. Discrete Math., 30 (2016), pp. 592–619]. Our result implies that [math] for all [math], making a step closer towards a conjecture of Thomassen [J. Graph Theory, 7 (1983), pp. 261–271] that [math], which was originally a result with a false proof and was the starting point of this research area.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Highly Connected Subgraphs with Large Chromatic Number\",\"authors\":\"Tung H. Nguyen\",\"doi\":\"10.1137/22m150040x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 243-260, March 2024. <br/> Abstract. For integers [math] and [math], let [math] be the least integer [math] such that every graph with chromatic number at least [math] contains a [math]-connected subgraph with chromatic number at least [math]. Refining the recent result of Girão and Narayanan [Bull. Lond. Math. Soc., 54 (2022), pp. 868–875] that [math] for all [math], we prove that [math] for all [math] and [math]. This sharpens earlier results of Alon et al. [J. Graph Theory, 11 (1987), pp. 367–371], of Chudnovsky [J. Combin. Theory Ser. B, 103 (2013), pp. 567–586], and of Penev, Thomassé, and Trotignon [SIAM J. Discrete Math., 30 (2016), pp. 592–619]. Our result implies that [math] for all [math], making a step closer towards a conjecture of Thomassen [J. Graph Theory, 7 (1983), pp. 261–271] that [math], which was originally a result with a false proof and was the starting point of this research area.\",\"PeriodicalId\":49530,\"journal\":{\"name\":\"SIAM Journal on Discrete Mathematics\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m150040x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m150040x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Highly Connected Subgraphs with Large Chromatic Number
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 243-260, March 2024. Abstract. For integers [math] and [math], let [math] be the least integer [math] such that every graph with chromatic number at least [math] contains a [math]-connected subgraph with chromatic number at least [math]. Refining the recent result of Girão and Narayanan [Bull. Lond. Math. Soc., 54 (2022), pp. 868–875] that [math] for all [math], we prove that [math] for all [math] and [math]. This sharpens earlier results of Alon et al. [J. Graph Theory, 11 (1987), pp. 367–371], of Chudnovsky [J. Combin. Theory Ser. B, 103 (2013), pp. 567–586], and of Penev, Thomassé, and Trotignon [SIAM J. Discrete Math., 30 (2016), pp. 592–619]. Our result implies that [math] for all [math], making a step closer towards a conjecture of Thomassen [J. Graph Theory, 7 (1983), pp. 261–271] that [math], which was originally a result with a false proof and was the starting point of this research area.
期刊介绍:
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.