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math.CO2019
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…
math.MG2019
4-regular planar unit triangle graphs without additional triangles
Mike Winkler, Peter Dinkelacker, Stefan Vogel
In this article we proof the existence of 4-regular planar unit-distance graphs consisting only of unit triangles without additional triangles. It is shown that the smallest number…