Regular hamiltonian embeddings of K_n,n and regular triangular embeddings of K_n,n,n

Knor, Martin and Širáň, Jozef (2008). Regular hamiltonian embeddings of K_n,n and regular triangular embeddings of K_n,n,n. Discrete Mathematics, 308(20) pp. 4796–4800.

DOI: https://doi.org/10.1016/j.disc.2007.08.069

Abstract

We give a group-theoretic proof of the following fact, proved initially by methods of topological design theory: Up to isomorphism, the number of regular hamiltonian embeddings of K_n,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of K_n,n.

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