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A tight bound for the number of edges of matchstick graphs

Lavollée, Jérémy and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2023) A tight bound for the number of edges of matchstick graphs. Discrete and Computational Geometry. ISSN 0179-5376

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Identification Number: 10.1007/s00454-023-00530-z


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:
Additional Information: © 2023 The Author(s)
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 13 Apr 2023 10:57
Last Modified: 19 May 2024 06:24

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