On scores, losing scores and total scores in hypertournaments

Shariefuddin Pirzada, Muhammad Ali Khan, Zhou Guofei, Koko K Kayibi


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 $s_{i}$ (losing score $r_{i}$) of a vertex $v_{i}$ is the number of arcs containing $v_{i}$ in which $v_{i}$ is not the last element (in which $v_{i}$ is the last element). The total score of $v_{i}$ is defined as $t_{i}=s_{i}-r_{i}$. In this paper we obtain stronger inequalities for the quantities $\sum_{i\in I}r_{i}$, $\sum_{i\in I}s_{i}$ and $\sum_{i\in I}t_{i}$, where $I\subseteq \{ 1,2,\ldots,n\}$. Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong $k$-hypertournaments.


Tournament, hypertournament, score, losing score, total score

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DOI: http://dx.doi.org/10.5614/ejgta.2015.3.1.2


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