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The minimum color‐degree perfect b‐matching problem (Col‐BM) is a new extension of the perfect b‐matching problem to edge‐colored graphs. The objective of Col‐BM is to minimize the maximum number of differently colored edges in a perfect b‐matching that are incident to the same node. We show that Col‐BM is NP‐hard on bipartite graphs by a reduction from (3,B2)‐Sat, and conclude that there exists no (2 − ϵ)‐approximation algorithm unless P=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.

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