Abstract
In this chapter we will consider the class of semicomplete multipartite digraphs (SMD). A digraph is semicomplete multipartite if it is obtained from a complete multipartite graph by replacing every edge by an arc or a pair of opposite arcs. In other words, the vertex set of a semicomplete multipartite digraph can be partitioned into sets such that vertices within the same set are nonadjacent and vertices between different sets are adjacent. This chapter gives a comprehensive survey on this class of digraphs.
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