随机图的f-染色的分类Ⅱ  

The Classification of f-coloring of Random GraphsⅡ

作　　者：蔡建生[1] 熊亚萍 CAI Jiansheng;XIONG Yaping(School of Mathematics and Information Science,Weifang University,Weifang,Shandong,261061,P.R.China;School of Mathematics and Statistics,Shandong Normal University,Ji'nan,Shandong,250358,P.R.China)

机构地区：[1]潍坊学院数学与信息科学学院,潍坊山东261061 [2]山东师范大学数学与统计学院,济南山东250358

出　　处：《数学进展》2021年第5期787-792,共6页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.12071351,11571258)。

摘　　要：随机图G(n,p)是具有n个标号的顶点的图,并且图中的每一对顶点以概率p被随机且独立地选择为图G的边.对于有顶点集V和边集E的简单图G=(V,E),G的f-染色c是广义的边染色,使每个颜色类在任一顶点v上至多出现f(v)次,其中f(v)是分配给v的正整数.在这篇文章中,我们给出随机图G(n,p)是f-第一类的一个充分条件.A random graph G(n,p)is a graph on n labeled vertices,in which every pair of vertices is chosen to be an edge of G randomly and independently with probability p.For a simple graph G=(V,E)with vertex set V and edge set E,an f-coloring c of G is a generalized edge-coloring in which each color class appears at each vertex v at most f(v)times,where f(v)is a positive integer assigned to v.In this paper,we give a sufficient condition for a random graph G(n,p)to be of f-class 1.

关 键 词：随机图 f-染色 Lovász局部引理 

分 类 号：O157.5[理学—数学]