图的最大亏格与直径

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。

Maximum Genus and Diameter of Graph

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.