新的上可嵌入图类  

New Classes of Upper Embeddable Graphs

作　　者：盛秀艳[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《重庆师范大学学报（自然科学版）》2004年第3期13-14,43,共3页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市教委科研基金项目(编号:010204)

摘　　要：一个连通图G的最大亏格γM(G)=(β(G)+ξ(G))/2,其中β(G)=|E(G)|-|V(G)|+1称为G的圈秩数,ξ(G)是G的Betti亏数。图G的C 划分是指:G的一个顶点划分{V1,V2,…,Vn},使得每个G[Vi]为多重完全图(1≤i≤n)。一个图的2 因子是指G的一个2 正则支撑子图F,若F为图G的一个2 因子。联系图的顶点划分和四边形2 因子的条件,本文给出了新的上可嵌入的图类。It is known that the maximum genus of a connected graph is γ_M(G)=(β(G)+ξ(G))/2,where β(G)=｜E(G)｜-｜V(G)｜+1 is the cycle rank of G,ξ(G) is the Betti dificiency of G.If there exists a partition {V_1,V_2,…,V_n} of V(G) such that G[V_i] is a multiple complete graph of each 1≤i≤n,then G has a C-partition.A 2-factor F of a graph G is a spanning subgraph of G such that d_F(v)=2 for any v∈V(F).Combining with the condition of C-partition and tetragon 2-factor,we give new classes of upper-embeddable graphs.

关 键 词：BETTI亏数 最大亏格 上可嵌入性 C-划分 四边形2-因子 连通图 

分 类 号：O157.5[理学—数学]