Extremal edge polytopes
Tuan Tran, G\"unter M. Ziegler
TL;DR
This paper investigates extremal properties of edge polytopes derived from finite graphs, focusing on vertex counts in k-neighborly cases and constructing polytopes with many facets.
Contribution
It determines maximum vertices for 2-, 3-, and 5-neighborly edge polytopes and constructs a family with exponentially many facets.
Findings
Maximum vertices for 2-, 3-, 5-neighborly edge polytopes identified.
Constructed a family of edge polytopes with exponentially many facets.
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 maximum 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.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · Advanced Graph Theory Research