一类图的强最大亏格嵌入

Strong Maximum Genus of Some Graphs

图的嵌入理论是拓扑图论中一个中心课题.图的最大亏格嵌入的刻画和研究已较完善.但对于强嵌入,这方面的讨论却很少.本文对于平面上的不含不交(指无公共节点)圈的图以及完全图K5,利用构造强最大亏格嵌入的方法,给出了强最大亏格.同时,也给出了完全二部图K3,k(k≥3)的不可定向强最大亏格的一个下界.

Embedding theory is a central subject in topological graph theory. There are many perfect results on maximum genera of graphs. But results on strong embeddings are far from the destination. In this paper, the strong maximum genera are presented as to the planar graphs without disjoint(no vertex in common) circuits and the complete graph of order 5 by constructing strong maximum genus embedding. And one lower bound of the strong maximum genus of the graph K3,k(k≥3) is shown too.