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Hamilton cycles in generalized Mycielski graphs
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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.
World Scientific Pub Co Pte Ltd
Title: Hamilton cycles in generalized Mycielski graphs
Description:
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.
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