Embeddings of 3-connected 3-regular planar graphs on surfaces of non-negative Euler characteristic [article]

Kengo Enami
2019 arXiv   pre-print
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
more » ... licit bounds for the number of inequivalent embeddings of G on each surface, and propose effective algorithms for enumerating and counting these embeddings.
arXiv:1806.11333v4 fatcat:prpn6af3uzdovbvmlgomhmwicm