Complexity of finding a join of maximum weight Original Research Article

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 finding a join of maximum weight: given a graph G and an edge weighting c : E(G)→R, find a join of maximum weight. We show that the problem is NP-hard even in the case of 0,1-weights, which answers a question of A. Frank in the negative. We also show that in the case of series–parallel graphs and arbitrary weights, the problem can be solved in time O(n3), where n is the number of vertices in G.