Preprint SCORES , INEQUALITIES AND REGULAR HYPERTOURNAMENTS
نویسنده
چکیده
Abstract. A k -hypertournament is a complete k -hypergraph with each k -edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a k hypertournament, the score si (losing score ri ) of a vertex vi is the number of edges containing vi in which vi is not the last element (in which vi is the last element). In this paper we obtain inequalities involving powers of scores and losing scores by using classical results from mathematical analysis (such as Hölder’s inequality) and show that equality holds if and only if the hypertournament is regular. We then use these inequalities to give a short proof of a result on the existence of regular hypertournaments. We also obtain an upper bound on the number of directed paths of length 2 in tournaments and hypertournaments, prove that the bound is sharp and that it is realized by regular hypertournaments.
منابع مشابه
On the scores and degrees in hypertournaments
A k-hypertournament H = (V,A), where V is the vertex set and A is an arc set, is a complete k-hypergraph with each k-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a k-hypertournament, the score si(losing score ri) of a vertex is the number of edges containing vi in which vi is not the last element(in which vi is the last element) and t...
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