Optimal Partition of a Bipartite Graph with prescribed layout into Non-Crossing b-Matchings

In this paper we deal with the problem of partitioning the edge set of a bipartite graph G=(L?R,E) with prescribed layout into the minimum number of non-crossing b-matchings. Some bounds and properties are discussed and an exact O(|E|loglogmin{|L|,|R|}) is presented for its solution.