# Applied Combinatorics, Dominance Order

Suppose four teams, the Aces, the Birds, the Cats, and the Dogs, played each other once. The Aces beat all three opponents except the Birds. The Birds lost to all opponents except the Aces. The Dogs beat the Cats. Represent the results of these games with a directed graph.

A dominance order is a listing of teams such that the ith team in the order beats the (i+1)th team. Find all dominance orders in the graph.

This is the directed graph for the teams, but I don't get the second part. Would a dominance order be ADCB?

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@curiousmind1995: It would not be a dominance order on the given set of teams. It would be a dominance order (and in fact the only one) on the subset $\{A,C,D\}$ of teams. – Brian M. Scott Oct 13 '15 at 19:58