3-regular matchstick graphs with given girth
Combinatorics
2014-01-20 v1
Abstract
We consider 3-regular planar matchstick graphs, i.e. those which have a planar embedding such that all edge lengths are equal, with given girth g. For girth 3 it is known that such graphs exist if and only if the number of vertices n is an even integer larger or equal to 8. Here we prove that such graphs exist for girth g=4 if and only if n is even and at least 20. We provide an example for girth g=5 consisting of 180 vertices.
Cite
@article{arxiv.1401.4360,
title = {3-regular matchstick graphs with given girth},
author = {Sascha Kurz and Giuseppe Mazzuoccolo},
journal= {arXiv preprint arXiv:1401.4360},
year = {2014}
}
Comments
18 pages, 1 table, 8 figures