Score lists in $[h$-$k]$-bipartite hypertournaments

Sh. Pirzada ; T. A. Chishti ; T. A. Naikoo

Diskretnaya Matematika, Tome 22 (2010) no. 1, pp. 150-157

Résumé

Let $m,n,h$ and $k$ be integers such that $m\geq h>1$ and $n\geq k>1$. An $[h$-$k]$-bipartite hypertournament on $m+n$ vertices is a triple $(U,V,E)$, with two vertex sets $U$ and $V$, $|U|=m$, $|V|=n$, together with an arc set $E$, a set of $(h+k)$-tuples of vertices, with exactly $h$ vertices from $U$ and exactly $k$ vertices from $V$, called arcs, such that for any $h$-subset $U_1$ of $U$ and $k$-subset $V_1$ of $V$, $E$ contains exactly one of the $(h+k)!$ $(h+k)$-tuples whose $h$ entries belong to $U_1$ and $k$ entries belong to $V_1$. We obtain necessary and sufficient conditions for a pair of nondecreasing sequences of nonnegative integers to be the losing score lists or score lists of some $[h$-$k]$-bipartite hypertournament.