| Unique Embeddings for Graphs on Orientable Surfaces Permitting Short Noncontractible Cycles |
| Received:September 12, 2002 |
| Key Words:
embedding representativity graph.
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| Fund Project:Supported by National Natural Science Found of China (10271048,19831080) and Shanghai Priority Academic Discipline. |
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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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