与直径和围长有关的最大亏格的下界  

The Lower Bounds of the Maximum Genus on Graphs in Terms of Diameter and Girth

作　　者：盛秀艳[1] 

机构地区：[1]聊城大学数学科学学院,聊城252059

出　　处：《数学学报（中文版）》2004年第6期1201-1204,共4页Acta Mathematica Sinica：Chinese Series

基　　金：重庆市教委科研基金项目(010204)

摘　　要：本文证明了如下结果:设G为直径为d的简单图,若G的围长不小于d,则当d为不小于4的偶数时,有ξ(G)≤1,即G是上可嵌入的;当d为不小于3的奇数时,有ξ(G)≤2,即γM(G)≥1/2β(G)-1.This paper proves the following results: Let G be a simple graph with diameter d. If its girth is not less than d, then the Betti deficient number of G, ξ(G)≤1, when d (≥4) is even, i.e. G is upper embeddable; and the Betti deficient number of G, ξ(G)≤2, when d (≥3) is odd, i.e. the maximum genus of G, γM(G)≥1/2β(G) - 1.

关 键 词：BETTI亏数 上可嵌入性 最大亏格 

分 类 号：O157.5[理学—数学]