Bases for the Matching Lattice of Matching Covered Graphs

This article contains a brief introduction to the theory of matching covered graphs: ear-decompositions, the matching lattice and the most important results of the theory. Its last section contains rather recent results and a conjecture relating the minimum number of double ears of any ear-decomposition of a matching covered graph and the number of bricks and bricks isomorphic to the Petersen graph in any brick decomposition of the same graph.

1995