Hamiltonian cycles in Cayley graphs whose order has few prime factors
Combinatorics
2015-03-17 v3
Abstract
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.
Cite
@article{arxiv.1009.5795,
title = {Hamiltonian cycles in Cayley graphs whose order has few prime factors},
author = {K. Kutnar and D. Marusic and D. W. Morris and J. Morris and P. Sparl},
journal= {arXiv preprint arXiv:1009.5795},
year = {2015}
}
Comments
44 pages, 1 figure, to appear in Ars Mathematica Contemporanea; new title and minor revisions suggested by the referees