在这份报纸,我们在 orientable 为局部地 嵌入LEW 的 3-connected 图 G 显示出那表面,下列结果 hold:1 )每如此的 embeddings 是最小的类嵌入; 2 )面部周期正是暗示如此的 embeddings 的唯一的导致的 nonseparating 周期; 3 )每重叠图 O ( G , C )是一张由两部组成的图, G 有一仅仅C桥 H 以便如果 C 是短的一个会缩的周期, C U H 比包含 C.This 的一个边的每个 noncontractible 周期延长的是 nonplanar
In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings; 3) Every overlap graph O(G, C) is a bipartite graph and G has only one C-bridge H such that C U H is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen's work on LEW-embedded graphs.