3 citations · 8 across the 14 of their papers we have counts for
4 papers · 1 filter
A 3-regular matchstick graph of girth 5 consisting of 54 vertices
Mike Winkler, Peter Dinkelacker, Stefan Vogel
In 2010 it was proved that a 3-regular matchstick graph of girth 5 must consist at least of 30 vertices. The smallest known example consisted of 180 vertices. In this article we co…
A catalog of 4-regular and (2;4)-regular matchstick graphs
Mike Winkler
The first part (page 1 - 7) of this article presents the currently known examples of 4-regular matchstick graphs with 63 - 70 vertices. The second part (page 8 - 15) presents the c…
On the existence of 4-regular matchstick graphs
Mike Winkler, Peter Dinkelacker, Stefan Vogel
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 verti…
Minimal completely asymmetric (4; n)-regular matchstick graphs
Mike Winkler, Peter Dinkelacker, Stefan Vogel
A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph $(m;n…