Decision problem for minimum interconnection trees in multipartite graphs is NP-complete but FPT in number of parts and polynomial-time on complete, quasi-complete, and t-quasi-complete graphs.
All your bases are belong to us: listing all bases of a matroid by greedy exchanges
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Complexity of Finding and Enumerating Interconnection Trees
Decision problem for minimum interconnection trees in multipartite graphs is NP-complete but FPT in number of parts and polynomial-time on complete, quasi-complete, and t-quasi-complete graphs.