English

On Cayley digraphs that do not have hamiltonian paths

Combinatorics 2013-06-25 v1

Abstract

We construct an infinite family of connected, 2-generated Cayley digraphs Cay(G;a,b) that do not have hamiltonian paths, such that the orders of the generators a and b are arbitrarily large. We also prove that if G is any finite group with |[G,G]| < 4, then every connected Cayley digraph on G has a hamiltonian path (but the conclusion does not always hold when |[G,G]| = 4 or 5).

Keywords

Cite

@article{arxiv.1306.5443,
  title  = {On Cayley digraphs that do not have hamiltonian paths},
  author = {Dave Witte Morris},
  journal= {arXiv preprint arXiv:1306.5443},
  year   = {2013}
}

Comments

10 pages, plus 14-page appendix of notes to aid the referee

R2 v1 2026-06-22T00:38:50.035Z