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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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1806.11333v3
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