Equitable coloring of planar graphs without 5-cycles and chordal 4-cycles
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Published:2024-01-22
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Wu Xianxi1ORCID,
Huang Danjun1ORCID
Affiliation:
1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Abstract
An equitable [Formula: see text]-coloring of a graph [Formula: see text] is a proper vertex coloring such that [Formula: see text] for any [Formula: see text], where [Formula: see text] ([Formula: see text]) is the set of vertices colored with [Formula: see text]. If there is an equitable [Formula: see text]-coloring of [Formula: see text], then the graph [Formula: see text] is said to be equitably [Formula: see text]-colorable. In this paper, we prove that every planar graph without 5-cycles and chordal 4-cycles has an equitable [Formula: see text]-coloring for [Formula: see text] where [Formula: see text] is the maximum degree of [Formula: see text].
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics