G的立方图G^3的上可嵌入性  

Upper-embeddability of a Graph G^3

作　　者：吴向群[1] 任韩[2] 

机构地区：[1]泉州师范学院数学系,福建泉州362000 [2]华东师范大学数学系,上海200062

出　　处：《沈阳师范大学学报（自然科学版）》2004年第4期248-251,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10271048).

摘　　要：自从Nordhaus,Stewart和White[1]等引入图的最大亏格以来,图的最大亏格以及图的上可嵌入引起了广泛关注.而图的最大亏格rM(G)是指最大的整数k使得图G的一个2 胞腔嵌入到可定向的曲面Sk上.因为图在任意可定向曲面上的2 胞腔嵌入中至少有一个面,关于图的上可嵌入性,刘彦佩[2],Xuong[3]和Nebseky[4]分别给出不同形式的充要条件.主要证明下述结果:设G是一个简单图,则G3是上可嵌入的.特别地,当k≥4时,Gk也是上可嵌入的.Since the introductory investigation of maximum genus by Nordhaus,Stewart and White[1],the up-embeddability fo graphs has been paid great attention so far.The maximum genus r_M(G) of a connected graph G is maximum integer k with the property that exists a celluar embedding of G on the orientable surface S_k of genus k.Since any celluar embedding must have at least one face,the Eluer polyhedral equation implies an upper bound on the maximum genus the number β(G) is known as the Betti number of the connected graph G.Liu[2],Xuong[3] and Nebesky[4] have independently provided different necessary and sufficient conditions on the upper embeddability of graphs.This paper mainly prove the following result:let G be a simple graph,then G^3 is up-embedable.Especially,if k≥4,then G^k are up-embedable as well.

关 键 词：图 最大亏格 BETTI亏数 上可嵌入 

分 类 号：O157.5[理学—数学]