应用数学2016，Vol.29Issue(2)：308-313,6.
可平面图的r-hued染色
On r-hued Coloring of Planar Graphs
摘要
Abstract
Let k,r be integers with k ＞ 0 and r ＞ 0.An r-hued coloring of a graph G is a proper k-coloring φ such that for any vertex v with degree d(v),v is adjacent to at least min{d(v),r} different colors.The r-hued chromatic number of G,xr(G),is the least integer k such that an r-hued coloring of G exists.In this paper,we show that if G is a planar graph withouti-cycles,4 ≤ i ≤ 9,then xr(G)≤ r + 5.This result implies that for a planar graph without 4-9 cycles,a conjecture on r-hued coloring of planar graphs holds.关键词
r-hued染色/可平面图/圈/Wagner猜想Key words
r-hued coloring/Planar graph/Cycles/Wagner's conjecture分类
数理科学引用本文复制引用
朱海洋,顾毓,盛景军,吕新忠..可平面图的r-hued染色[J].应用数学,2016,29(2):308-313,6.基金项目
Supported by the National Natural Science Foundation of China(61170302) （61170302）
