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arXiv · 2108.07522

Bounding the number of edges of matchstick graphs

Jérémy Lavollée·Konrad J. Swanepoel
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Abstract

We show that a matchstick graph with $n$ vertices has no more than $3n-c\sqrt{n-1/4}$ edges, where $c=\frac12(\sqrt{12} + \sqrt{2π\sqrt{3}})$. The main tools in the proof are the Euler formula, the isoperimetric inequality, and an upper bound for the number of edges in terms of $n$ and the number of non-triangular faces. We also find a sharp upper bound for the number of triangular faces in a matchstick graph.

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BibTeXRIS

Jérémy Lavollée, Konrad J. Swanepoel. 2021-08-17. Bounding the number of edges of matchstick graphs. https://arxiv.org/abs/2108.07522

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