# Title: Extremal questions about matchstick graphs and penny graphs

## Speaker: Konrad Swanepoel, London School of Economics

## Date and time: 2pm (New York time), Tuesday, April 4, 2023

## Place: On Zoom (details provided on the seminar mailing list)

A penny graph is the intersection graph of a packing of circles of
diameter 1. These graphs, also called minimum-distance graphs, were
introduced by Erdös in 1946, who asked for the maximum possible number
of edges in a penny graph with $n$ vertices. This problem was fully
solved by Harborth in 1974, who in turn introduced the more general
notion of a matchstick graph. A matchstick graph is a plane graph
drawn with straight-line segments of unit length. Harborth conjectured
in 1986 that the same maximum number of edges occurs for matchstick
graphs as for penny graphs. I will discuss this conjecture, recently
solved, and a number of related unsolved extremal problems.

Joint work with Jérémy Lavollée.