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 | log log min { | L | , | R | } ) is presented for its solution.