Author’s abstract: ”A simple characterization of the set MCOLOOP of coloops in the strict matching matroid of an undirected graph \(G=(V,E)\) is provided, which allows the Edmonds decomposition of G to be produced in \(O(| V|^{5/2})\). Based on this decomposition, we have the following results: Two graphs associated with G are produced in \(O(| V| +| E|)\). One is a bipartite graph with at most \(3| E|\) edges, whose transversal matroid is isomorphic to the strict matching matroid of G; the other is a directed graph with at most \(| E|\) edges, representing the strict gammoid dual to the strict matching matroid. The matroid components of the strict matching matroid of G are produced in \(O(| V| +\delta k(G)(k(G)-\delta))\), where \(\delta\) is the matching defect of G and k(G) is the number of components of G(V-MCOLOOP). We show how to list the bases of the strict matching matroid of G, and also calculate its Whitney and Tutte polynomials, in \(O(N\delta [(| V| -\delta)^ 2+| E|])\), where N is the number of bases in the matroid.”