In this paper we present an overview of several techniques we have studied over the years to build game AI for domination games. Domination is a game style in which teams compete for control of map locations, and has been very popular over the years. Due to the rules of the games, good performance is mostly dependent on overall strategy rather than the skill of individual team members. Hence, t...

We introduce the domination search game which can be seen as a natural modiica-tion of the well-known node search game. Various results concerning the domination search number of a graph are presented. In particular, we establish a very interesting connection between domination graph searching and a relatively new graph parameter called dominating target number.

The domination game on a graph G (introduced by B. Brešar, S. Klavžar, D.F. Rall [1]) consists of two players, Dominator and Staller, who take turns choosing a vertex from G such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible, and Staller wishes to delay this process as much as po...

A Roman dominating function on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value w(f) = ∑ v∈V f(v). The Roman domination number of a graph G, denoted by γR(G), equals the minimum weight of a Roman dominating function on ...

BackgroundGame Theory Interpretation MethodsRandomizationFunctional Lagrange Multipliers ConclusionsReferences

The domination game played on a graph G consists of two players, Dominator and Staller who alternate taking turns choosing a vertex from G such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible and Staller wishes to delay the process as much as possible. The game domination number γg...

In a graph G, a vertex is said to dominate itself and its neighbors. The Domination game is a two player game played on a finite graph. Players alternate turns in choosing a vertex that dominates at least one new vertex. The game ends when no move is possible, that is when the set of chosen vertices forms a dominating set of the graph. One player (Dominator) aims to minimize the size of this se...