每条弧都在Hamilton-路上的半完全多部有向图

Semicomplete multipartite digraphs whose every arc is contained in Hamiltonian path

用一条弧或一对方向相反的弧代替完全多部无向图的每一条边所得到的有向图被称为半完全多部有向图。2002年L.Volkmann[6]提出这样一个问题:给出半完全多部有向图中每一条弧都在Hamilton-路上的充分条件。论文针对此问题给出了一个新的充分条件,并举例说明了该充分条件的独立性以及它在某种意义下的最佳可能性。

A semieomplete 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 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 muhipartite digraphs demonstrating that this sufficient condition is independent and in some sense,it is best posssible.