Unique Embeddings for Graphs on Orientable Surfaces Permitting Short Noncontractible Cycles
Received:September 12, 2002  
Key Word: embedding   representativity   graph.  
Fund ProjectL:Supported by National Natural Science Found of China (10271048,19831080) and Shanghai Priority Academic Discipline.
Author NameAffiliation
REN Han Dept. of Math.
East China Normal University
Shanghai
China 
LIU Yan-pei Dept. of Math.
Northern Jiaotong University
Beijing
China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2004.04.007
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