Hamiltonian cycles in certain graphs

Abstract

Abstract It is observed that arrays which arise in the scheduling of tournaments exist if and only if there are Hamiltonian cycles in certain graphs. The graphs are generalizations of those which arise in the “Footballers of Croam” problem. It is proven that such Hamiltonian cycles exist in infinite classes of the graphs. Subject classification ( Amer. Math. Soc. ( MOS ) 1970 ): 05 C 35, 05 B 30.