We study biased Maker-Breaker games on a graph system {G1,…,Gs}, in which Maker's goal is to claim certain rainbow structures, i.e., specified subgraphs consisting of at most one edge from each graph Gi. We consider the rainbow connectivity game, in which Maker wants to claim a rainbow path between every pair of vertices.
We analyse this game, determining the threshold bias when it is played on systems of complete graphs, up to a constant factor. As a byproduct, we find the order of the threshold bias for the Maker-Breaker diameter game, and disprove a conjecture by Balogh, Martin and Pluhár.
Milica Maksimović (Université de Novi Sad)
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