Explicit representations by halfspaces of the edge cone of a graph

TL;DR

This paper provides explicit geometric representations of the edge cone of any simple graph using finite intersections of halfspaces, with detailed facet descriptions for bipartite connected graphs.

Contribution

It introduces a novel explicit representation of the edge cone for arbitrary graphs and characterizes facets for bipartite connected graphs.

Findings

Explicit finite intersection representations of the edge cone.

Facet descriptions for bipartite connected graphs.

Canonical irreducible representation for bipartite connected graphs.

Abstract

Let G be an arbitrary simple graph. The main results are explicit representations of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a canonical irreducible representation.