摘要
一个图称为是1-可嵌入曲面的,当且仅当它可以画在一个曲面上,使得它的任何一条边最多交叉另外一条边.x′(G)和△(G)分别表示图G的边色数和最大度.给定图G是1-可嵌入到欧拉示性数x(∑)≥0的曲面∑上的图.如果△(G)≥8且不含4-圈或者△(G)≥7且围长g(G)≥4,则图G满足等式△(G)=x′(G),其中,g(G)表示图G中最短圈的长度.
A graph is 1-embedded on a surface if it can be drawn on the surface so that each edge is crossed by at most one other edge. χ'(G) and △(G) denote the chromatic index and the maximum degree of G, respectively. Let G be l-embedded on a surface of Euler characteristic χ(∑)≥ 0. The paper shows that △(G) = χ'(G) if △(G) ≥ 8 and G contains no 4-cycles or A(G) ≥ 7 and g(G)≥ 4, where, g(G) denotes the length of the shortest cycle in G.
出处
《应用数学学报》
CSCD
北大核心
2016年第1期12-20,共9页
Acta Mathematicae Applicatae Sinica
基金
新疆维吾尔自治区高校科研计划(XJEDU2014S067)资助项目
关键词
欧拉示性数
4-圈
围长
边色数
放电法
Euler characteristic
4-cycles
girth
the chromatic index
discharging method