Unique Embeddings for Graphs on Orientable Surfaces Permitting Short Noncontractible Cycles

可定向曲面上具有较短不可收缩圈图嵌入的唯一性(英文)

A fundamental result in topological graph theory by H.Whitney states that a 3-connected graph has at most one planar embedding. C.Thomassen generalized this to LEW-embeddings on higher surfaces. We establish several unique embedding results for 3-connected graphs on orientable surfaces which admit relatively large facial walks and rcpresentativity and hence generalize Thomassen's uniqueness theorem on LEW-embeddings.

拓扑图论中的一个基本问题就是要决定图在一个(可定向)曲面上的嵌入之数目(既嵌入的柔性问题).H.Whitney的经典结果表明:一个3-连通图至多有一个平面嵌入;C.Thomassen的LEW-嵌入(大边宽度)理论将这一结果推广到一般的可定向曲面.本文给出了几个关于一般可定向曲面上嵌入图的唯一性定理.结果表明:一些具有大的面迹的可定向嵌入仍然具有唯一性.这在本质上推广了C.Thomassen在LEW-嵌入方面的工作.