Complexity of Finding a Join of Maximum Weight

A subset of edges J E(G) in a undirected graph G is called a join if at most half the edges of each cycle of G are contained in J . In this paper we consider the problem of nding a join of maximum weight: given a graph G and an edge weighting c : E(G) ! R, nd a join of maximum weight. We show that the problem is NPhard even in the case of 0; 1-weights, which answers in the negative a question of A. Frank. We also show that in the case of series-parallel graphs and arbitrary weights the problem can be solved in time O(n ), where n is the number of vertices in G