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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
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)
