7 citations · 7 across the 6 of their papers we have counts for
4 papers · 1 filter
The Erdős unit distance problem for small point sets
Boris Alexeev, Dustin G. Mixon, Hans Parshall
We improve the best known upper bound on the number of edges in a unit-distance graph on vertices for each . When , our bounds match the best kn…
Linear programming bounds for cliques in Paley graphs
Mark Magsino, Dustin G. Mixon, Hans Parshall
The Lovász theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a ma…
Small unit-distance graphs in the plane
Aidan Globus, Hans Parshall
We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilaka…
Embedding distance graphs in finite field vector spaces
Alex Iosevich, Hans Parshall
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complet…