New minimal (4; n)regular matchstick graphs
Abstract
A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and nonadjacent edges do not intersect. We call a matchstick graph ($m;n)$regular if every vertex has only degree $m$ or $n$. In this article the authors present the latest known $(4;n)$regular matchstick graphs for $4\leq n\leq11$ with a minimum number of vertices.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.07134
 Bibcode:
 2016arXiv160407134W
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Combinatorics
 EPrint:
 23 pages, 25 figures, 43 matchstick graphs. [v5] contains a new minimal graph for n=11 with 771 edges