Konrad Swanepoel

Matchstick graphs in the plane and on the sphere

Matchstick graphs are non-crossing unit-distance graphs drawn in the plane. They were introduced by Heiko Harborth in the 80s, who posed some extremal questions about them. Matchstick graphs can be generalised to other spaces if we replace unit straight-line segments by equal-length non-crossing geodesic segments. In this talk we plan to discuss some recent results on matchstick graphs in the plane and on the sphere. Some of this is joint work with Jérémy Lavollée.