On the existence of 4-regular matchstick graphs
Mike Winkler, Peter Dinkelacker, Stefan Vogel · arXiv (Cornell University) · 2017
A matchstick graph is a planar unit-distance graph. We call it \emph{4-regular} if every vertex has degree 4. While examples of 4-regular matchstick graphs with fewer than 63 vertices are known only for $n \in \{52, 54, 57, 60\}$, we prove the existence of such graphs for every integer $n \geq 63$.