We consider tournaments defined by several linear orderings of the vertex set according to some rule specifying the direction of each arc depending only on the order of the end vertices in each of the orderings. In the finite case, it was proved in Alon et al. (J Comb Theory Ser B 96:374-387, 2006) that the domination number of such tournaments is bounded in terms of the rule only. We show that for infinite tournaments, under some natural restrictions, the domination number is always finite, though in general cannot be bounded. We give some sufficient conditions under which there exists an upper bound in terms of the rule and/or the order types, and provide examples demonstrating that the bounds obtained are not very far from truth.
展开▼
机译：我们考虑根据某些规则指定的各个弧的方向，这些规则由顶点集的几种线性顺序定义的比赛，这些规则仅取决于每个顺序中最终顶点的顺序。在有限情况下，Alon等人证明了这一点。 （J Comb Theory Ser B 96：374-387，2006），此类比赛的统治数仅受规则限制。我们表明，对于无限比赛，在某些自然限制下，支配数始终是有限的，尽管通常不能限制。我们给出了一些足够的条件，在这些条件下，在规则和/或订单类型方面存在一个上限，并提供了一些示例，这些示例表明所获得的界限离真相不是很远。
展开▼
