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局部大边宽嵌入图的面圈和C-桥的结构(英文)
Structures of Facial Cycles and C-bridges of Embedded Graphs with Locally LEW-embedding Properties
【摘要】 <正>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 CUH 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.
【Abstract】 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 CUH 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.
【Key words】 (locally)LEW-embedding； C-bridge； overlap graph；
- 【文献出处】 数学季刊 ,Chinese Quarterly Journal of Mathematics , 编辑部邮箱 ,2008年04期
- 【分类号】O157.5
- 【下载频次】33