A constructive solution to a problem of ranking tournaments
نویسندگان
چکیده
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Solution of a covering problem related to labelled tournaments
Suppose we have a tournament with edges labelled so that the edges incident with any vertex have at most k distinct labels (and no vertex has outdegree 0). Let m be the minimal size of a subset of labels such that for any vertex there exists an outgoing edge labelled by one of the labels in the subset. It was known that m ? k+1 2 for any tournament. We show that this bound is almost best possib...
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متن کاملRanking Tournaments
A tournament is an oriented complete graph. The feedback arc set problem for tournaments is the optimization problem of determining the minimum possible number of edges of a given input tournament T whose reversal makes T acyclic. Ailon, Charikar and Newman showed that this problem is NP-hard under randomized reductions. Here we show that it is in fact NP-hard. This settles a conjecture of Bang...
متن کاملA Problem on Tournaments
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 . O...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111613