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 non-adjacent 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 $4\le n\le 11$ with a minimum number of vertices.

23 pages, 25 figures, 43 matchstick graphs. [v5] contains a new minimal graph for n=11 with 771 edges

References in corpus (2)

• Minimal Polynomials for the Coordinates of the Harborth Graph
• 3-regular matchstick graphs with given girth

Cited by in corpus (2)

• On the existence of 4-regular matchstick graphs
• Minimal completely asymmetric (4; n)-regular matchstick graphs