Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth
Combinatorics
2019-02-28 v1
Abstract
It is well known that 3--regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3--regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1--, 2-- or 3--edge-connected depending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3--regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.
Keywords
Cite
@article{arxiv.1902.10344,
title = {Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth},
author = {Michael Haythorpe},
journal= {arXiv preprint arXiv:1902.10344},
year = {2019}
}