Abstract:The necessary and sufficient conditions for the existence of a 1-rotational k-cycle system of the complete graph K v are established. The proof provides an algorithm able to determine, directly and explicitly, an odd k-cycle system of K v whenever such a system exists. q
Abstract:In this article, it is proved that for each even integer m ≥ 4 and each admissible value n with n > 2m, there exists a cyclic m-cycle system of K n , which almost resolves the existence problem for cyclic m-cycle systems of K n with m even. q
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