Hamiltonian decomposition of prisms over cubic graphs
Authors: Moshe Rosenfeld 1; Ziqing Xiang 2
NULL##NULL
Moshe Rosenfeld;Ziqing Xiang
1 Institute of Technology (UW, Tacoma)
2 Department of Computer Science
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.