In any tournament, with the players partitioned any way into two groups called Winners and Losers, we define two measures: is the number of vertex pairs consisting of a labeled “loser” and a “winner” where the loser beats the winner, and similarly
is the number of such pairs where the loser has at least as many total wins as the winner. We prove that
and this bound is tight. The result has a natural interpretation and easy generalization in the domain of majorization.
By: Nikhil Bansal; Don Coppersmith; Gregory B. Sorkin
Published in: RC24107 in 2006
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