Hamiltonian Embeddings from Triangulations
نویسندگان
چکیده
A Hamiltonian embedding of Kn is an embedding of Kn in a surface, which may be orientable or non-orientable, in such a way that the boundary of each face is a Hamiltonian cycle. Ellingham and Stephens recently established the existence of such embeddings in non-orientable surfaces for n = 4 and n 6. Here we present an entirely new construction which produces Hamiltonian embeddings of Kn from triangulations of Kn when n ≡ 0 or 1 (mod 3). We then use this construction to obtain exponential lower bounds for the numbers of nonisomorphic Hamiltonian embeddings of Kn.
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