Niche graphs and mixed pair graphs of tournaments

In our efforts to study the niche graph of a tournament T, we have found it easier to study the complement, which we call the "mixed pair" graph of T and denote MP(T). We show that an undirected graph G is MP(T), for some tou rnament T, if and only if G is one of the following: a cycle of odd order, a path of even order, a forest of odd order consisting of two paths, a fore st of even order consisting of three paths, or a forest of four or more pat hs. (In this description, we consider an isolated vertex to be a path.) (C) 1999 John Wiley & Sons, Inc.