Existence of a regular unimodular triangulation of the edge polytopes of finite graphs

TL;DR

This paper provides criteria for determining when the edge polytope of a finite graph admits a regular unimodular triangulation, and applies these criteria to various graph examples.

Contribution

It introduces new criteria based on graph data for the existence of regular unimodular triangulations of edge polytopes.

Findings

Criteria successfully identify graphs with regular unimodular triangulations

Application to multiple graph examples confirms the criteria's effectiveness

Enhances understanding of the geometric properties of graph polytopes

Abstract

In this paper we give several criteria for the edge polytope of a fundamental FHM-graph to possess a regular unimodular triangulation in terms of some simple data of the the graph. We further apply our criteria to several examples of graphs and show that their edge polytopes possess a regular unimodular triangulation.