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Quasi-hamiltonian paths in semicomplete multipartite digraphs. (English) Zbl 1262.05095
Summary: A quasi-hamiltonian path in a semicomplete multipartite digraph \(D\) is a path which visits each maximal independent set (also called a partite set) of \(D\) at least once. This is a generalization of a hamiltonian path in a tournament.
In this paper we investigate the complexity of finding a quasi-hamiltonian path, in a given semicomplete multipartite digraph, from a prescribed vertex \(x\) to a prescribed vertex \(y\) as well as the complexity of finding a quasi-hamiltonian path whose end vertices belong to a given set of two vertices \(\{ x,y\} \). While both of these problems are polynomially solvable for semicomplete digraphs (here all maximal independent sets have size one), we prove that the first problem is NP-complete and describe a polynomial algorithm for the latter problem.

MSC:
05C45 Eulerian and Hamiltonian graphs
05C20 Directed graphs (digraphs), tournaments
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