Niche graphs and mixed pair graphs of tournaments
Steve Bowser, Charles A. Cable, Richard Lundgren · Journal of Graph Theory · 1999
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 tournament 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 forest of even order consisting of three paths, or a forest of four or more paths. (In this description, we consider an isolated vertex to be a path.) © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 319–332, 1999