2024/02/21 by Divakaran, Athira, James, Tijo, Klavžar, Sandi +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.13581
In the Maker-Breaker domination game, Dominator and Staller play on a graph G by taking turns in which each player selects a not yet played vertex of G. Dominator's goal is to select all the vertices in a dominating set, while Staller aims to prevent this from happening. In this paper, the game is investigated on corona products of graphs. Its outcome is determined as a function of the outcome of the game on the second factor. Staller-Maker-Breaker domination numbers are determined for arbitrary corona products, while Maker-Breaker domination numbers of corona products are bounded from both sides. All the bounds presented are demonstrated to be sharp. Corona products as well as general graphs with small (Staller-)Maker-Breaker domination numbers are described.