Vesna Iršič: Total domination game

Povzetek. The total domination game was introduced by Henning et al. in 2015 as a game played on a graph G by two players, Dominator and Staller, who alternate taking turns for as long as possible. On each turn one chooses such a vertex in G that totally dominates at least one not yet totally dominated vertex. Dominator tries to minimize and Staller tries to maximize the number of moves. The total number of selected vertices is called the game total domination number, \gamma_{tg}(G). In this talk we present some known results about the game, especially the effect of vertex predomination on the game total domination number.