7 papers
Sharp Threshold for Cliques in Random 0/1 Polytope Graphs
Catherine Babecki, Tycho Elling, Asaf Ferber
We study graph-theoretic properties of random polytopes. Specifically, let be a random subset where each point is included independently with prob…
Sparse Graphical Designs via Linear Programming
Hessa Al-Thani, Catherine Babecki, J. Carlos Martínez Mori
Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical desi…
Spectrahedral Geometry of Graph Sparsifiers
Catherine Babecki, Stefan Steinerberger, Rekha R. Thomas
We propose an approach to graph sparsification based on the idea of preserving the smallest eigenvalues and eigenvectors of the Graph Laplacian. This is motivated by the fact t…
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.…
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…
Codes, Cubes, and Graphical Designs
Catherine Babecki
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in parti…
Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs
Catherine Babecki, Chris Jennings-Shaffer, Geoffrey Sangston
We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduc…