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