Minimumcolor-degreeperfectb-matchings

The minimum color-degree perfectb-matching problem (Col-BM) is a new extension of the perfectb-matching problem to edge-colored graphs. The objective of Col-BM is to minimize the maximum number of differently colored edges in a perfectb-matching that are incident to the same node. We show that Col-BM isNP-hard on bipartite graphs by a reduction from (3,B2)-Sat, and conclude that there exists no(2 - epsilon)-approximation algorithm unlessP=NP. However, we identify a class of two-colored complete bipartite graphs on which we can solve Col-BM in polynomial time. Furthermore, we use dynamic programming to devise polynomial-time algorithms solving Col-BM with a fixed number of colors on series-parallel graphs and simple graphs with bounded treewidth.