J. Bang-Jensen and A. Yeo, Strongly connected spanning subgraphs with the minimum number of arcs in semicomplete multipartite digraphs, submitted.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....uses a new characterization of a longest cycle in an extended semicomplete digraph. In the last section we point out the our methods imply that the MSSS problem can be solved efficiently for a much larger superclass of semicomplete digraphs than just quasi transitive digraphs. We remark that in [9], the MSSS problem was solved for various generalizations of tournaments. In particular polynomial algorithms were given for the classes of extended semicomplete digraphs and semicomplete bipartite digraphs. Furthermore, it was conjectured in [9] that the MSSS problem is also polynomially solvable ....

....just quasi transitive digraphs. We remark that in [9] the MSSS problem was solved for various generalizations of tournaments. In particular polynomial algorithms were given for the classes of extended semicomplete digraphs and semicomplete bipartite digraphs. Furthermore, it was conjectured in [9] that the MSSS problem is also polynomially solvable for general semicomplete multipartite digraphs. 2 Terminology We shall always use the number n to denote the number of vertices in the digraph currently under consideration. Digraphs are finite, have no loops or multiple arcs. We use V (D) and ....

J. Bang-Jensen and A. Yeo, Strongly connected spanning subgraphs with the minimum number of arcs in semicomplete multipartite digraphs, submitted.

....6.6 The MSSS problem is solvable in time O(n 5 2 p log n) for semicomplete bipartite digraphs. If we only want an O(n 3 ) algorithm, then this follows rather straightforwardly from an algorithmic interpretation of the proofs of Lemmas 6.1 6.4 and Theorem 6.5. 7 Remarks and open problems In [19] the MSSS problem was solved for quasi transitive digraphs another generalization of tournaments for which the hamiltonian cycle problem is polynomial, but non trivial (a digraph is quasi transitive if whenever xy and yz are arcs, there is also an arc between x and z) It was shown that the MSSS ....

J. Bang-Jensen, J. Huang and A. Yeo, Strongly connected spanning subgraphs with the minimum number of arcs in quasi-transitive digraphs (1999), submitted.

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