Adjacency of the best and second best valued solutions in combinatorial optimization problems

The authors say that a polytope satisfies the strong adjacency property if every best valued extreme point of the polytope is adjacent to some second best valued extreme point for any weight vector. Perfect matching polytopes satisfy this property. In this paper, the authors give sufficient conditions for a polytope to satisfy the strong adjacency property. From this, binary b-matching polytopes, set partitioning polytopes, set packing polytopes, etc. satisfy the strong adjacency property.