How to search a tree to which Eulerian networks are attached

We call a network partly Eulerian if consists of a tree (of length a and radius r) to which a nite number of disjoint Eulerian networks (of total length b) are attached, each at a single point. We show that for such networks, a search strategy consisting equiprobably of a minimal (Chinese Postman) covering path and its reverse path is optimal, in the sense that it minimizes (at a + b=2