On scores, losing scores and total scores in hypertournaments

Electronic Journal of Graph Theory and Applications

Zhou Guofei¹  Koko K Kayibi²  Muhammad Ali Khan³  Shariefuddin Pirzada⁴ 

[1] Nanjing University;Qatar University;University of Calgary;University of Kashmir;

关键词: tournament, hypertournament, score, losing score, total score;   

DOI  :  10.5614/ejgta.2015.3.1.2

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown