Matching Minors

In this final chapter of Part I, we bring together ideas of bicontractions of vertices of degree two and deletions of removable classes described in the preceding chapters to introduce two closely related types of minors that are specific to the theory of matching covered graphs. They play a role in this subject that is similar to that of the familiar type of minors in graph theory.We consider first the more general of these two types of minors which was introduced by Norine and Thomas (2007, [78]).