Extremal edge polytopes

Abstract

The 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.