The numbers of edges of the order polytope and the chain polytope of a finite partially ordered set

Abstract Let P be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope 풪 ( P ) is equal to that of the chain polytope C ( P ) . Furthermore, it will be shown that the degree sequence of the finite simple graph which is the 1 -skeleton of 풪 ( P ) is equal to that of C ( P ) if and only if 풪 ( P ) and C ( P ) are unimodularly equivalent.