ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 64,   1   (1995)
pp.   77-81

A NOTE ON THE HAMILTONIAN GENUS OF A COMPLETE BIPARTITE GRAPH
A. DEMOVIC

Abstract.  The Hamiltonian genus of a graph $G$ (denoted by $\gamma_H(G)$) is the smallest number $g$ such that the graph $G$ is embeddable in the orientable surface with genus $g$ and there is some face-boundary $b$ which is a Hamiltonian cycle of $G$. In this paper we show that \lceil (n-2)(n-1)/4 \rceil \leq \gamma_H(K_n,n) \leq \lceil n/2 \rceil^2 + \lceil n/2 \rceil.

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