| The degree partition of a simple graph is its degree sequence rearranged in a weakly decreasing order. Let DP(n) (respectively, DS(n) denote the convex hull of all degree partitions (respectively, degree sequences) of simple graphs on the vertex set [n]=1,2, ,n. We think of DS(n) as the symmetrization of DP(n) and DP(n) as the asymmetric part of DS(n). The polytope DS(n) is a well studied object (Koren, Beissinger and Peled, Peled and Srinivasan, Stanley). In this paper we study the polytope DP(n) and determine its vertices (and, as a corollary, its volume), edges, and facets. |