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Hamiltonian decomposition of prisms over cubic graphs

Abstract : The prisms over cubic graphs are 4-regular graphs. The prisms over 3-connected cubic graphs are Hamiltonian. In 1986 Brian Alspach and Moshe Rosenfeld conjectured that these prisms are Hamiltonian decomposable. In this paper we present a short survey of the status of this conjecture, various constructions proving that certain families of prisms over 3-connected cubic graphs are Hamiltonian decomposable. Among others, we prove that the prisms over cubic Halin graphs, cubic generalized Halin graphs of order 4k + 2 and other infinite sequences of cubic graphs are Hamiltonian decomposable.
Keywords : Graph theory
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Moshe Rosenfeld, Ziqing Xiang. Hamiltonian decomposition of prisms over cubic graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 16 no. 2 (in progress) (2), pp.111--124. ⟨hal-01185619⟩

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