2023/06/09 by Duchêne, Eric, Dumas, Arthur, Oijid, Nacim +2 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.05728
We study the Maker-Maker version of the domination game introduced in 2018 by Duchêne et al. Given a graph, two players alternately claim vertices. The first player to claim a dominating set of the graph wins. As the Maker-Breaker version, this game is PSPACE-complete on split and bipartite graphs. Our main result is a linear time algorithm to solve this game in forests. We also give a characterization of the cycles where the first player has a winning strategy.