Extremal Edge Polytopes

Tuan Tran, Günter M. Ziegler


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.


0/1-polytopes; edge polytopes of graphs; subpolytopes of a hypersimplex; extremal f-vectors; number of facets; Turán numbers; pseudorandom graphs

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