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

Knor, Martin and Širáň, Jozef (2008). Regular hamiltonian embeddings of Kn,n and regular triangular embeddings of Kn,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 Kn,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 Kn,n.

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