On the graphic matroid parity problem
A new proof is given of the min-max theorem of Lovász on the graphic matroid problem. The proof is based on existing proofs of Tutte's matching theorem. A matroid is graphic if it is the cycle matroid of some graph. Given a graph \(G\) and a partition \(V\) of its edge set into pairs, \((G, V)\) is called a \(v\)-graph, and a \(v\)-forest of \((G, V)\) is a forest of \(G\) consisting of \(v\)-pairs in \(V\). The graphic matroid problem is to find the maximum number of \(v\)-pairs in a \(v\)-forest in a \(v\)-graph.
scientific article; zbMATH DE number 1965031
scientific article