A tight bound for the number of edges of matchstick graphs

Lavollée, Jérémy and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2024) A tight bound for the number of edges of matchstick graphs. Discrete and Computational Geometry, 72. 1530–154. ISSN 0179-5376

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Abstract

A matchstick graph is a plane graph with edges drawn as unit-distance line segments. Harborth introduced these graphs in 1981 and conjectured that the maximum number of edges for a matchstick graph on n vertices is ⌊3n−√12n-3⌋. In this paper we prove this conjecture for all n≥1. The main geometric ingredient of the proof is an isoperimetric inequality related to L’Huilier’s inequality.

Item Type:	Article
Official URL:	https://www.springer.com/journal/454
Additional Information:	© 2024 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Apr 2023 10:57
Last Modified:	19 Nov 2024 14:03
URI:	http://eprints.lse.ac.uk/id/eprint/118619

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