caa a22 4500 445813687 CHVBK 20180317145219.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s11083-010-9159-z doi (NATIONALLICENCE)springer-10.1007/s11083-010-9159-z Fon-Der-Flaass D. Institute of Mathematics, Novosibirsk, Russia aut Domination Number of Certain Infinite Tournaments [Elektronische Daten] [D. Fon-Der-Flaass] 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. Springer Science+Business Media B.V., 2010 Tournament nationallicence Domination number nationallicence Well ordering nationallicence Order Springer Netherlands 28/1(2011-03-01), 157-161 0167-8094 28:1<157 2011 28 11083 https://doi.org/10.1007/s11083-010-9159-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9159-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fon-Der-Flaass D. Institute of Mathematics, Novosibirsk, Russia aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/1(2011-03-01), 157-161 0167-8094 28:1<157 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer