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A Tight Bound for the Number of Edges of Matchstick Graphs
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Journal Article
A Tight Bound for the Number of Edges of Matchstick Graphs
2024
Overview
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.
Publisher
Springer Nature B.V
Subject
