Year: 2014
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kurz, Sascha, Mazzuoccolo, Giuseppe
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1619909423