Hamiltonian cycles in Cayley graphs whose order has few prime factors

K. Kutnar; D. Marusic; D. W. Morris; J. Morris; P. Sparl

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arXiv · 1009.5795

Hamiltonian cycles in Cayley graphs whose order has few prime factors

K. Kutnar·D. Marusic·D. W. Morris·J. Morris·P. Sparl

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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.

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BibTeX RIS

K. Kutnar, D. Marusic, D. W. Morris, J. Morris, P. Sparl. 2011-04-04. Hamiltonian cycles in Cayley graphs whose order has few prime factors. https://arxiv.org/abs/1009.5795

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