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math.CO2024
A New Class of Geometrically Defined Hypergraphs Arising from the Hadwiger Nelson Problem
Sean Fiscus, Eric Myzelev, Hongyi Zhang
There is a famous problem in geometric graph theory to find the chromatic number of the unit distance graph on Euclidean space; it remains unsolved. A theorem of Erdos and De-Bruij…
math.CO2024
Characterization of Colorings Obtained by a Method of Szlam
Eric Myzelev
Szlam's Lemma began life as a way of getting upper bounds on the chromatic numbers of distance graphs in normed vector spaces. Now analogs are available in a variety of hypergraph…