连通图的最大亏格的下界

Lower Bound for the Maximum Genus of Connected Graphs

一个连通图G的最大亏格γM(G)可由其Betti亏数ξ(G)确定。利用图的匹配数和围长给出了Betti亏数的上界,进而得到了最大亏格的下界,而且该下界是可达的。

The maximum genus of a connected graph is determined by its Betti deficiency. In this paper we establish a upper bound for the Betti deficiency in terms of the matching number and the girth of a graph, and thus give a lower bound for the maximum genus. Meantime we show that the lower bound is achievable.