Existence of a regular unimodular triangulation of the edge polytopes of   finite graphs
  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. 
Ginji Hamano
math.CO