On complementary coverage of Ωn(T)

Every acyclic Birkhoff polytope is represented by a bicolored tree. In this paper we use the concept of T-component of a tree in order to cover it. In addition, the definitions of T-edge cover (respectively, T-vertex cover) subgraphs and of complementary coverage by vertices (edges) are introduced. Some consequences related to the dimension of the acyclic Birkhoff polytope are also obtained.