Hamilton cycles in generalized Mycielski graphs

Let mu(m)(G) denote the generalized Mycielski graph of G. In this paper, it is proved that for k >= 1, if G has k pairwise edge-disjoint Hamilton cycles, then mu(m)(G) has left ceiling [k/2] right ceiling Hamilton cycles which are pairwise edge-disjoint. Further, it is shown that if G has k pairwise edge-disjoint Hamilton cycles with |V (G)| >= 4k - 4 for k >= 4 and |V (G)| >= 4k - 3 for k <= 3, then mu(m)(G) has k pairwise edge-disjoint Hamilton cycles. Finally it is shown that mu(m)(G) is hamiltonian even when G is non-hamiltonian with a specified 2-factor. Consequently, the Mycielski graph of Flower Snark graph Jn, for all odd n >= 3, is Hamiltonian.