%0 Journal Article
%T Maximum Genus, Degree of Vertex and Girth<br>最大亏格、点度和围长
%A OUYANG Zhangdong
%A REN Junfeng
%A HUANG Yuanqiu
%A <br>欧阳章东
%A 任俊峰
%A 黄元秋
%J 系统科学与数学
%D 2009
%I 
%X Let G be a graph. Denote by g(G) the girth of G, and by \delta(G) the minimum degree of G. The following two results are proved:1) Let G be a k-edge-connected simple graph, for any cycle C, there exist a vetex x\in C satisfying the condition:d_G(x)>\frac{|V(G)|}{(k-1)^2+2}+k-g(G)+2, k=1,2,3, then G is upper embeddable, and the lower bound is best possible.2) Let G be a k-edge- connected simple graph, then \xi(G)\le \max\{1,m\}, k=1, \max\{1,\frac{1}{k-1}m-1\},k=2,3, where m=\frac{|V(G)|g(G)-6}{g(G)^{2}+(\delta(G)-2)g(G)-4}.Moreover, the upper bound is best possible, and a better lower bound of the maximum genus is given.
%K Graph
%K Betti deficiency number
%K upper embeddability
%K cycle<br>图
%K Betti亏数
%K 上可嵌入性
%K 圈
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=E1C35CC836523D7EED5FD1D55FD478AD&yid=DE12191FBD62783C&vid=771469D9D58C34FF&iid=38B194292C032A66&sid=A5111BA190517959&eid=3356A7630A93A219&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=9