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arXiv · 1703.03148

On Hamilton Cycle Decompositions of Tensor Products of Graphs

P. Paulraja·S. Sampath Kumar
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Abstract

A Hamiltonian decomposition of $G$ is a partition of its edge set into disjoint Hamilton cycles. Manikandan and Paulraja conjectured that if $G$ and $H$ are Hamilton cycle decomposable circulant graphs with at least one of them is nonbipartite, then their tensor product is Hamilton cycle decomposable. In this paper, we have proved that, if $G$ is a Hamilton cycle decomposable circulant graph with certain properties and $H$ is a Hamilton cycle decomposable multigraph, then their tensor product is Hamilton cycle decomposable. In particular, tensor products of certain sparse Hamilton cycle decomposable circulant graphs are Hamilton cycle decomposable.

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P. Paulraja, S. Sampath Kumar. 2017-03-09. On Hamilton Cycle Decompositions of Tensor Products of Graphs. https://arxiv.org/abs/1703.03148

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