A Decomposition of 2-Weak Vertex-packing Polytopes

The 2{weak vertex-packing polytope of a loopless graph G with d vertices is the subset of the unit d{cube satisfying x i + x j 1 for every edge (i; j) of G. The dilation by 2 of this polytope is a polytope P with integral vertices. We triangulate P with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral group B d. This labeling gives rise to a shelling of the triangulation b P of P, where the h{vector of b P (and the Ehrhart h {vector of P) can be computed as a descent statistic on a subset of B d deened in terms of G. A recursive way of computing the h{vector of b P is also given, and a recursive formula for the volume of P.