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math.CO2022
A combinatorial bound on the number of distinct eigenvalues of a graph
Sarah Allred, Craig Erickson, Kevin Grace +2
The smallest possible number of distinct eigenvalues of a graph , denoted by , has a combinatorial bound in terms of unique shortest paths in the graph. In particular, $q(…
math.CO2019
Self-Polar Polytopes
Alathea Jensen
Self-polar polytopes are convex polytopes that are equal to an orthogonal transformation of their polar sets. These polytopes were first studied by Lovász as a means of establishin…
math.CO2018
Intersections, circuits, and colorability of line segments
Boris Brimkov, Jesse Geneson, Alathea Jensen +2
We derive sharp upper and lower bounds on the number of intersection points and closed regions that can occur in sets of line segments with certain structure, in terms of the numbe…