关于直径为4的图的最大亏格

On the Maximum Genus of Graphs with Diameter Four

该文证明了如下结果 :设 G为直径为 4的简单图 ,若 G不含 3阶完全子图 K3,则 G的 Betti亏数ξ( G)≤ 4,因此有 G的最大亏格γM( G)≥ 12 β( G) -

This paper proves the following results: Let G be a simple graph with diameter four, if G does not contain the complete subgraph \$K\-\{3\}\$ of order three, then the Betti deficient number of \$G,ξ(G)≤4\$, and thus the maximum genus of \$G,γ\-\{M\}(G)≥12β(G)-2.\$