江苏师范大学学报(自然科学版)
江囌師範大學學報(自然科學版)
강소사범대학학보(자연과학판)
Journal of Xuzhou Normal University(Natural Science Edition)
2014年
3期
22-26
,共5页
无圈边色数%平面图%最大度%圈
無圈邊色數%平麵圖%最大度%圈
무권변색수%평면도%최대도%권
acyclic edge coloring%planar graph%maximum degree%cycle
一个图G的无圈边染色是一个正常的边染色,使得不产生双色圈.Fiamˇcik 和Alon等分别提出了著名的无圈边色数猜想:每一个简单图G是无圈边(Δ+2)可染的,其中Δ是G的最大度.证明了对于不含3圈和5圈相邻的平面图猜想成立.
一箇圖G的無圈邊染色是一箇正常的邊染色,使得不產生雙色圈.Fiamˇcik 和Alon等分彆提齣瞭著名的無圈邊色數猜想:每一箇簡單圖G是無圈邊(Δ+2)可染的,其中Δ是G的最大度.證明瞭對于不含3圈和5圈相鄰的平麵圖猜想成立.
일개도G적무권변염색시일개정상적변염색,사득불산생쌍색권.Fiamˇcik 화Alon등분별제출료저명적무권변색수시상:매일개간단도G시무권변(Δ+2)가염적,기중Δ시G적최대도.증명료대우불함3권화5권상린적평면도시상성립.
An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are pro-duced.The acyclic chromatic index a′(G)of G is the smallest k such that G has an acyclic edge coloring using k col-ors.Fiamˇcik and Alon et al,independently,made a conjecture that every simple graph G has a′(G)≤Δ+2,whereΔdenotes the maximum degree of G.In this paper,this conjecture for planar graphs G without a 3-cycle adjacent to a 5-cycle are confirmed.