Packing circuits in eulerian digraphs (Q1924492)

A digraph is eulerian if for every vertex \(v\) its invalency equals its outvalency. Let \(G\) be a eulerian digraph. If \(H\) can be obtained from a subgraph of \(G\) by contracting edges then \(H\) is a minor of \(G\). Suppose \(c\) is the maximum number of pairwise edge-disjoint directed circuits of \(G\) and \(t\) the smallest size set of edges that meets all directed circuits of \(G\). The author shows that if \(G\) is a eulerian digraph such that the underlying undirected graph has no minor in the Peterson family then \(c=t\).