Hamiltonian cycles in Cayley graphs whose order has few prime factors

Details Hamiltonian cycles in Cayley graphs whose order has few prime factors Hamiltonian cycles in Cayley graphs whose order has few prime factors

2010-09-29

arxiv.org/abs/1009.5795v3

Mathematics

Combinatorics

44 pages, 1 figure, to appear in Ars Mathematica Contemporanea; new title and minor revisions suggested by the referees

Scientific paper

We prove that if Cay(G;S) is a connected Cayley graph with n vertices, and
the prime factorization of n is very small, then Cay(G;S) has a hamiltonian
cycle. More precisely, if p, q, and r are distinct primes, then n can be of the
form kp with k < 32 and k not equal to 24, or of the form kpq with k < 6, or of
the form pqr, or of the form kp^2 with k < 5, or of the form kp^3 with k < 3.

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