Maximum Rainbow Matching is polynomial-time solvable if almost every color class is complete multipartite and NP-hard otherwise.
Another look at the degree constrained subgraph problem.Information Processing Letters, 12(2):89–92
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A Complexity Dichotomy for Generalized Rainbow Matchings Based on Color Classes
Maximum Rainbow Matching is polynomial-time solvable if almost every color class is complete multipartite and NP-hard otherwise.