Strongly quasi-Hamiltonian-connected semicomplete multipartite digraphs

Strongly quasi-Hamiltonian-connected semicomplete multipartite digraphs

A semicomplete multipartite or semicomplete c-partite digraph D is a biorientation of a c-partite graph. A semicomplete multipartite digraph D is called strongly quasiHamiltonian-connected, if for any two distinct vertices x and y of D, there is a path P from x to y such that P contains at least one vertex from each partite set of D. In this paper we show that every 4-strong semicomplete multip...

Quasi-hamiltonian paths in semicomplete multipartite digraphs

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 prescrib...

Kings in semicomplete multipartite digraphs

A digraph obtained by replacing each edge of a complete p-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicom-plete p-partite digraph, or just a semicomplete multipartite digraph. A semicomplete multipartite digraph with no cycle of length two is a multipartite tournament. In a digraph D, an r-king is a vertex q such that every vertex in D ...

Strongly connected spanning subgraphs with the minimum number of arcs in semicomplete multipartite digraphs

We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strongly connected subgraph of a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamiltonian cycle problem. We characterize the number of arcs in a minimum spanning strong subgraph for digraphs which are either extended semicomplete or semicomplete bipartite. Our ...

Cycles in Semicomplete Multipartite Digraphs