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math.CO2022
Eigenpolytope Universality and Graphical Designs
Catherine Babecki, David Shiroma
We show that the eigenpolytopes of graphs are universal in the sense that every polytope, up to affine equivalence, appears as the eigenpolytope of some positively weighted graph.…
math.CO2022
Graphical Designs and Gale Duality
Catherine Babecki, Rekha R. Thomas
A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality…