Semicomplete multipartite digraphs whose every arc is contained in Hamiltonian path
Shengjia Li · Computer Engineering and Applications Journal · 2007
A semicomplete multipartite digraph is obtained by replacing each edge of a complete multipartite graph by an arc or by a pair of two mutually opposite arcs.In 2002,L.Volkmann 6 raised a problem:determine other sufficient conditions for semicomplete multipartite digraphs such that every arc is contained in a Hamiltonian path.In this paper,we give a new sufficient condition and describe some semicomplete multipartite digraphs demonstrating that this sufficient condition is independent and in some sense,it is best posssible.