关于最大亏格达到下界的三连通三正则简单图(英文)

On 3-connected cubic graphs whose maximum genus attains the lower bound

已被证明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 ,当节点数可被三整除时 ,这个下界可以达到 本文提供了达到最大亏格下界的三连通三正则简单图所具有特殊结构 。

It is known that every 3 connected cubic graph has the maximum genus at least one third of its cycle rank.When the number of vertices is zero modulo three,the bound is tight.In this paper,we provide the structure of a 3 connected cubic graph whose maximum genus attains the lower bound.If the maximum genus of a 3 connected cubic graph is one third of its cycle rank,it has a triangle 2 factor.