# Pakanun Dokyeesun: Maker-Breaker domination game on Cartesian products of graphs

Date of publication: 13. 4. 2023

Discrete mathematics seminar

Tuesday

18

April

Time:

10:15

Location:

Plemljev seminar, Jadranska 19

**Abstract.** The Maker-Breaker domination game is played on a graph *G* by two players, called Dominator and Staller. They alternately select an unplayed vertex in *G*. Dominator wins the game if he forms a dominating set while Staller wins the game if she claims all vertices from a closed neighborhood of a vertex in the graph. Recently, Forcan and Qi studied the Maker-Baker domination game on Cartesian products of graphs. It was shown that if Dominator wins the *D*-game and *S*-game on *G*, then Dominator also wins the game on the Cartesian product of *G* and *H* for any arbitrary *H*. In our work, we will show who is the winner of the game on the product of paths, stars, and complete bipartite graphs and how fast he/she wins.