Hamiltonian decompositions of Cayley graphs on abelian groups of even order

  • Authors:

  • Jiuqiang Liu

  • Affiliations:

  • Department of Mathematics, Eastern Michigan University, Ypsilanti, MI

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2003

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Abstract

Alspach conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In 1992, the author proved that the conjecture holds if S = {s1, s2, ..., sk} is a minimal generating set of an abelian group A of odd order. Here we prove an analogous result for abelian group of even order: If A is a finite abelian group of even order at least 4 and S = {s1, s2, ..., sk} is a strongly minimal generating set (i.e., 2si ∉ 〈S - {si}〉 for each 1≤i≤k) of A, then cay(A,S) can be decomposed into hamiltonian cycles.