4 papers · 1 filter
A Topological Figiel-Lindenstrauss-Milman Theorem and its Applications
Florian Frick, Kaave Hosseini, Eric Myzelev +2
We prove a topological generalization of the Figiel--Lindenstrauss--Milman inequality, answering a recent question of Frick, Hosseini, and Vasileuski: every nonempty strongly regul…
A New Dominating Set Game on Graphs
Sean Fiscus, Glenn Hurlbert, Eric Myzelev +1
We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vert…
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…
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…