Claw-free cubic graphs are (1,1,2,2)-colorable

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-03-14 DOI:10.1016/j.disc.2025.114477

Boštjan Brešar , Kirsti Kuenzel , Douglas F. Rall

引用次数: 0

Abstract

(1, 1, 2, 2)

-coloring of a graph is a partition of its vertex set into four sets two of which are independent and the other two are 2-packings. In this paper, we prove that every claw-free cubic graph admits a

(1, 1, 2, 2)

-coloring. This implies that the conjecture from Brešar et al. (2017) [5] that the packing chromatic number of subdivisions of subcubic graphs is at most 5 is true in the case of claw-free cubic graphs.

查看原文本刊更多论文

无爪立方图是(1,1,2,2)可着色的

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.