Clustered coloring of (path + 2K1)-free graphs on surfaces

IF 1.2 1区 数学 Q1 MATHEMATICS Journal of Combinatorial Theory Series B Pub Date : 2025-02-13 DOI:10.1016/j.jctb.2025.02.001
Zdeněk Dvořák
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引用次数: 0

Abstract

Esperet and Joret proved that planar graphs with bounded maximum degree are 3-colorable with bounded clustering. Liu and Wood asked whether the conclusion holds with the assumption of the bounded maximum degree replaced by assuming that no two vertices have many common neighbors. We answer this question in positive, in the following stronger form: Let Pt be the complete join of two isolated vertices with a path on t vertices. For any surface Σ, a subgraph-closed class of graphs drawn on Σ is 3-choosable with bounded clustering if and only if there exists t such that Pt does not belong to the class.
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来源期刊
CiteScore
2.70
自引率
14.30%
发文量
99
审稿时长
6-12 weeks
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
期刊最新文献
Editorial Board Some results and problems on tournament structure Ramsey numbers of bounded degree trees versus general graphs Tree amalgamations and quasi-isometries Clustered coloring of (path + 2K1)-free graphs on surfaces
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