151 citations · 649 across the 52 of their papers we have counts for
57 papers
A tight bound for the number of edges of matchstick graphs
Jérémy Lavollée, Konrad Swanepoel
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…
The number of small-degree vertices in matchstick graphs
Jérémy Lavollée, Konrad J. Swanepoel
A matchstick graph is a crossing-free unit-distance graph in the plane. Harborth (1981) proposed the problem of determining whether there exists a matchstick graph in which every v…
Contacts in totally separable packings in the plane and in high dimensions
Márton Naszódi, Konrad J. Swanepoel
We study the contact structure of totally separable} packings of translates of a convex body in , that is, packings where any two touching bodies have a separatin…
Bounding the number of edges of matchstick graphs
Jérémy Lavollée, Konrad J. Swanepoel
We show that a matchstick graph with vertices has no more than edges, where . The main tools in the proof are the E…
Angular measures and Birkhoff orthogonality in Minkowski planes
Márton Naszódi, Vilmos Prokaj, Konrad Swanepoel
Let and be two unit vectors in a normed plane . We say that is Birkhoff orthogonal to if the line through in the direction supports the unit d…
Outer linear measure of connected sets via Steiner trees
Konrad J. Swanepoel
We resurrect an old definition of the linear measure of a metric continuum in terms of Steiner trees, independently due to Menger (1930) and Choquet (1938). We generalise it to any…