2024/06/21 by James, Tijo, Klavžar, Sandi, Kuziak, Dorota +2 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.15108
The Maker-Breaker resolving game is a game played on a graph G by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex of G. The goal of Resolver is to select all the vertices in a resolving set of G, while that of Spoiler is to prevent this from happening. The outcome o(G) of the game played is one of R, S, and N, where o(G)=R (resp. o(G)=S), if Resolver (resp. Spoiler) has a winning strategy no matter who starts the game, and o(G)=N, if the first player has a winning strategy. In this paper, the game is investigated on corona products G\odot H of graphs G and H. It is proved that if o(H)∈\N, S\, then o(G\odot H) = S. No such result is possible under the assumption o(H) = R. It is proved that o(G\odot Pk) = S if k=5, otherwise o(G\odot Pk) = R, and that o(G\odot Ck) = S if k=3, otherwise o(G\odot Ck) = R. Several results are also given on corona products in which the second factor is of diameter at most 2.