2025/12/03 by Nathan Bowler, Bowler, Nathan, Henri Ortmüller +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2512.03664
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
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. For a t ∈ ℕ, let K2,t denote the K2,t together with the edge connecting the two vertices in the partition class of size 2. The purpose of this paper is to give a winning strategy for P1 in the game R(Kℵ0, K2,3).