Hamilton cycles in generalized Mycielski graphs

Abstract

Let [Formula: see text] denote the generalized Mycielski graph of [Formula: see text]. In this paper, it is proved that for [Formula: see text], if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles, then [Formula: see text] has [Formula: see text] Hamilton cycles which are pairwise edge-disjoint. Further, it is shown that if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles with [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], then [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles. Finally it is shown that [Formula: see text] is hamiltonian even when [Formula: see text] is non-hamiltonian with a specified [Formula: see text]-factor. Consequently, the Mycielski graph of Flower Snark graph [Formula: see text], for all odd [Formula: see text], is Hamiltonian.