Edge exchanges in Hamiltonian decompositions of Kronecker-product graphs

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Abstract

Let G be a connected graph on n vertices, and let α, β, γ and δ be edge-disjoint cycles in G such that (i) α, β (respectively, γ.δ) are vertex-disjoint and (ii) |α| + \β\ = |γ| + |δ| = n, where |α| denotes the length of α. We say that α, β, γ and δ yield two edge-disjoint Hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e, f, g and h such that each of (α - {e}) ∪ (β - {f}) ∪ {g, h} and (γ - {g}) ∪ (δ - {h}) ∪ {e, f} constitutes a Hamiltonian cycle in G. We show that if G is a nonbipartite, Hamiltonian decomposable graph on an even number of vertices which satisfies certain conditions, then Kronecker product of G and K2 as well as Kronecker product of G and an even cycle admits a Hamiltonian decomposition by means of appropriate edge exchanges among smaller cycles in the product graph.

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APA

Jha, P. K., Agnihotri, N., & Kumar, R. (1996). Edge exchanges in Hamiltonian decompositions of Kronecker-product graphs. Computers and Mathematics with Applications, 31(2), 11–19. https://doi.org/10.1016/0898-1221(95)00189-1

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