Extremal Edge Polytopes
Keywords: 0/1-polytopes, edge polytopes of graphs, subpolytopes of a hypersimplex, extremal f-vectors, number of facets, Turán numbers, pseudorandom graphs
AbstractThe "edge polytope" of a finite graph $G$ is the convex hull of the columns of its vertex-edge incidence matrix. We study extremal problems for this class of polytopes. For $k =2, 3, 5$ we determine the maximal number of vertices of $k$-neighborly edge polytopes up to a sublinear term. We also construct a family of edge polytopes with exponentially-many facets.