Clustered colouring of graph classes with bounded treedepth or pathwidth

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Combinatorics, Probability & Computing Pub Date : 2020-12-10 DOI:10.1017/S0963548322000165

S. Norin, A. Scott, D. Wood

引用次数: 4

Abstract

The "clustered chromatic number" of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$. We determine the clustered chromatic number of any minor-closed class with bounded treedepth, and prove a best possible upper bound on the clustered chromatic number of any minor-closed class with bounded pathwidth. As a consequence, we determine the fractional clustered chromatic number of every minor-closed class.

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具有有界树深或路径宽度的图类的聚类着色

一类图的“聚类色数”是最小整数$k$，使得对于某些整数$c$，该类中的每个图都是$k$-可着色的，其单色分量的大小最多为$c$。我们确定了树深有界的任意小闭类的聚类色数，并证明了路径宽度有界的任意小闭类的聚类色数的最佳可能上界。因此，我们确定了每个小闭类的分数簇色数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.