二连通三正则简单图的最大亏格及结构性质(英文)

Maximum genus and structures of 2-connected cubic simplicial graphs

摘要: 已知二连通三正则简单图的最大亏格至少为其圈秩的三分之一 .且 ,此下界可以达到 .本文表明这种达到最大亏格下界的图具有特殊结构 ,而且其节点数可被三整除 .同时 ,还证明了当节点数不可被三整除时 ,这种图最大亏格的下界可提高一个亏格 .

Abstract: It is known that the lower bound on the maximum genus of a 2 connected cubic simplicial graph is at least one third of its cycle rank.This bound is tight.This paper has showed that there is a special structure in such a graph that its maximum genus attains the lower bound,and the order of such a graph is zero modulo three.When the order of a 2 connected cubic simplicial graph is not zero modulo three,it is found that its maximum genus is at least one third of its cycle rank plus one.