mad(G)≤13/4的图的均匀染色  

Equitable coloring of graphs with mad(G)≤

作　　者：吴弦禧 黄丹君[1] WU Xianxi;HUANG Danjun(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,Zhejiang,China)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004

出　　处：《山东大学学报(理学版)》2025年第2期41-50,62,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12171436)。

摘　　要：图G的均匀k-染色是图G的一个正常k-点染色且满足任意2个色类的顶点数之差的绝对值至多为1。若G存在一个均匀k-染色,则称G是均匀k-可染的。图G的最大平均度是图G的所有非空子图的平均度的最大值,用mad(G)表示。本文运用权转移的方法证明mad(G)≤13/4的图是均匀k-可染的,其中k≥max{Δ(G),6},且Δ(G)是图G的最大度。An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most one.The graph G is said to be equitably k-colorable if G has an equitable k-coloring.The maximum average degree is the maximum value of average degree of all nonempty subgraphs of G,denoted by mad(G).In this paper,we utilizes the method of weight trans-13 fer to prove that a graph G with mad(G)≤13/4 is equitably k-colorable fork≥max{Δ(G),6},where△(G)is the maximum degree 4 of G.

关 键 词：均匀k-染色 最大平均度 权转移方法 

分 类 号：O157.5[理学—数学]