Relaxed equitable colorings of planar graphs with girth at least 8

被引：3
|
作者：
Li, Ming [1 ]
Zhang, Xia [1 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Peoples R China
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Equitable coloring; Relaxed coloring; Discharging; Planar graph; DEFECTIVE COLORINGS;
D O I：
10.1016/j.disc.2019.111790
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An RE-m-coloring of a graph G is a vertex m-coloring of G, which is relaxed (every vertex shares the same color with at most one neighbor) and equitable (the sizes of all color classes differ by at most one). In this article, we prove that every planar graph with minimum degree at least 2 and girth at least 8 has an RE-m-coloring for each integer m >= 4. We use the discharging method and Hall's Theorem to simply the structures of counterexamples. (C) 2019 Elsevier B.V. All rights reserved.
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页数：7
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