Can I read Bounding the Number of Edges of Matchstick Graphs on EtoBox?

Bounding the Number of Edges of Matchstick Graphs by Lavollée, Jérémy; Swanepoel, Konrad J. is a scholarly article available to read on EtoBox.

What is Bounding the Number of Edges of Matchstick Graphs about?

We show that a matchstick graph with $n$ vertices has no more than $3n-c\sqrt{n-1/4}$ edges, where $c=\frac12(\sqrt{12} + \sqrt{2\pi\sqrt{3}})$. 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.

Author

Lavollée, Jérémy; Swanepoel, Konrad J.

Published

2021

Language

EN