Representations of bicircular matroids (Q1179188)

Let \(G=(V,E)\) be a graph and for \(I\subseteq E\) define \(G[I]\) to be the edge-induced subgraph of \(G\). The collection \(\{I\subseteq E\mid\) each component of \(G[I]\) has at most one cycle\} is the collection of independent sets of a matroid \(M\) on \(E\). This matroid \(M\) is called the bicircular matroid. The graph \(G\) is a representation of \(M\). This paper describes a relationship between bicircular matroids and the class of linear-programming problems known as generalized network flow problems and contains results on matrix representations of bicircular matroids.