Abstract
We define a class Γ of 4-regular Cayley graphs on abelian groups and prove every element of Γ to be decomposable into two Hamiltonian cycles. This result is a special case of a conjecture ofB. Alspach and includes a theorem ofJ.-C. Bermond et al. as a subcase.
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References
B. Alspach. Unsolved problem 4.5.Ann. Discrete Math. 27 (1985), 464.
J.-C. Bermond, O. Favaron andM. Maheo. Hamilton decomposition of Cayley graphs of degree 4.J. Comb. Theory B46 (1989), 142–153.
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Baumann, U., Lesch, M. & Schmeichel, I. A note on Hamiltonian decompositions of Cayley graphs. Abh.Math.Semin.Univ.Hambg. 65, 105–111 (1995). https://doi.org/10.1007/BF02953317
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DOI: https://doi.org/10.1007/BF02953317