A characterization of the graphs in which the transversal number equals the matching number

Let G be a graph without loops. The matching number v(G) is the cardinality of a largest matching (maximum matching) in G. The transversal number T(G) is the cardinality of a smallest set of vertices meeting all the edges of G (such a set is called a transversal) (cf. [I]). Obviously T(G) 3 v(G). The graphs for which equality holds can be characterized by excluded configurations (in some special sense), as follows.