Packing circuits in matroids (Q1013971)

The aim of the paper is to present a characterization of the matroids that satisfy a given minimax relation concerning packing circuits in matroids, namely a characterization of all good matroids. The proposed characterization contains a solution to the 2-edge-connected subgraph polyhedra problem introduced by Cornuejols et al. in 1985 and solved by \textit{D. Vandenbussche} and \textit{G. L. Nemhauser} [J. Comb. Optim. 9, No. 4, 357--379 (2005; Zbl 1093.90051)]. The authors define as well the notion of good graphs and establish as well several characterizations of the good matroids and good graphs: a structural characterization of the good matroids based on decomposition, the property that being a good graph is preserved under summing operation, the equivalence between the truncatable graphs and good graphs. The proposed approach is different from those already developed in the literature.