典型文献
Majority Coloring of r-Regular Digraph
文献摘要：
A majority k-coloring of a digraph D with k colors is an assignment c:V(D)→{1,2,…,k},such that for every v∈V(D),we have c(w)=c(v)for at most half of all out-neighbors w∈N+(v).For a natural number k≥2,a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours.Kreutzer,Oum,Seymour,van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring.Gir?o,Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1/k-majority(2k-1)-coloring.We showed that every r-regular digraph D with r＞361n(2n)has a majority 3-coloring and proved that every digraph D with minimum outdegree δ+＞2k2(2k-1)2/(k-1)2 ln[(2k-1)n]has a 1/k-majority(2k-1)-coloring.And we also proved that every r-regular digraph D with r＞3k2(2k-1)/(k-1)2 ln(2n)has a 1/k-majority(2k-1)-coloring.
文献关键词：
中图分类号：
作者姓名：
XIA Wei-hao;SHI Mei;XIAO Ming-yue;CAI Jian-sheng;WANG Ji-hui
作者机构：
School of Mathematical Sciences,University of Jinan,Jinan 250022,China;School of Mathematics and Information Sciences,Weifang University,Weifang 261061,China
文献出处：
引用格式：
[1]XIA Wei-hao;SHI Mei;XIAO Ming-yue;CAI Jian-sheng;WANG Ji-hui-.Majority Coloring of r-Regular Digraph)[J].数学季刊（英文版）,2022(02):142-146
A类：
Digraph,Kreutzer,Oum,Zypen,Gir,Kittipassorn,Popielarz,361n,outdegree,2k2,3k2
B类：
Majority,Coloring,Regular,majority,coloring,digraph,colors,is,assignment,such,that,every,have,most,half,all,neighbors,N+,For,natural,number,vertices,each,vertex,receives,same,proportion,neighbours,Seymour,van,der,Wood,proved,has,conjectured,admits,We,showed,regular,2n,minimum,ln,And,also
AB值：
0.310524
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