Embeddings of 3-connected 3-regular planar graphs on surfaces of non-negative Euler characteristic release_txk4vpej4ng4ndfwcvxszrywhu

by Kengo Enami

Released as a article .

2019  

Abstract

Whitney's theorem states that every 3-connected planar graph is uniquely embeddable on the sphere. On the other hand, it has many inequivalent embeddings on another surface. We shall characterize structures of a 3-connected 3-regular planar graph G embedded on the projective-plane, the torus and the Klein bottle, and give a one-to-one correspondence between inequivalent embeddings of G on each surface and some subgraphs of the dual of G embedded on the sphere. These results enable us to give explicit bounds for the number of inequivalent embeddings of G on each surface, and propose effective algorithms for enumerating and counting these embeddings.
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Type  article
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Date   2019-09-05
Version   v3
Language   en ?
arXiv  1806.11333v3
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