A Problem on Tournaments
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چکیده
By a tournament we mean the outcome of a round-robin tournament in which there are no draws . Such a tournament may be represented by a graph in which the n players are represented by vertices labelled 1, 2, . . . , n, and the outcomes of the games are represented by directed edges so that every pair of vertices is joined by one directed edge . We call such a graph a complete directed graph . One can also represent such a tournament by an nXn matrix T = (t .,) in which t 1~ ij is 1 if i beats j, and 0 otherwise, so that T is a (0, 1) matrix with t . + t„ = 1 for i / j and (by definition) t . . = 0 . 1 3 3 1 11
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تاریخ انتشار 1964