The Matching Lattice and Optimal Ear Decompositions

The objective of this chapter is to present a characterization of the matching lattice of a matching covered graph. Our approach to this characterization, envisaged by Lovász as explained in Section 13.1, makes essential use of Theorem 15.1. This approach also enables us to answer two related questions; one concerning bases of the matching lattices, and the other concerning optimal ear decompositions of matching covered graphs. In the last section we give a description of the ‘dual’ approach adopted by Lovász [58].