图的最大亏格与直径  

Maximum Genus and Diameter of Graph

作　　者：赵靖[1] 梁开福[1] 

机构地区：[1]湘潭大学,湖南湘潭411105

出　　处：《廊坊师范学院学报（自然科学版）》2012年第4期17-20,23,共5页Journal of Langfang Normal University(Natural Science Edition)

摘　　要：设G是直径为4的简单图,若G不含3阶完全子图K3,则G的Betti亏数ξ(G)≤2,即G的最大亏格γM(G)≥1/2β(G)-1,并且不等式的下界是可达的。这种结合图的直径等条件的证明方法改进了相关结果。Combined the condition of the diameter of a graph, the paper proves the following results; Let G be a simple graph with diameter four, if G does not contain the complete subgraph K3 of order three, then the Betti deficient number of G,ξ（G）≤2,and thus the maximurm genus of G,γM（G）≥1/2β（G）-1,And the lower bound is best possible. And some relative results are improved.

关 键 词：图 BETTI亏数 上可嵌入性 直径 

分 类 号：O157.5[理学—数学]