2025/12/18 by Bowler, Nathan, Ortmüller, Henri
#05C57 #91A46 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.16722
The Strong Ramsey game R(B,G) is a two player game with players P1 and P2, where B and G are k-uniform hypergraphs for some k ≥ 2. G is always finite, while B may be infinite. P1 and P2 alternately color uncolored edges e ∈ B in their respective color and P1 begins. Whoever completes a monochromatic copy of G in their own color first, wins the game. If no one claims a monochromatic copy of G in a finite number of moves, the game is declared a draw. In this paper, we give an infinite set of 3-uniform hypergraphs \Gt\t ≥ 3, such that P2 has a drawing strategy in the Strong Ramsey game R(Kℵ0(3), Gt). This improves a result by David, Hartarsky and Tiba.