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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.03664 |
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| _version_ | 1866909941839691776 |
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| author | Bowler, Nathan Ortmüller, Henri |
| author_facet | Bowler, Nathan Ortmüller, Henri |
| contents | The Strong Ramsey game $\mathcal{R}(B,G)$ is a two player game with players $P_1$ and $P_2$, where $B$ and $G$ are $k$-uniform hypergraphs for some $k \geq 2$. $G$ is always finite, while $B$ may be infinite. $P_1$ and $P_2$ alternately color uncolored edges $e \in B$ in their respective color and $P_1$ 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 $t \in \mathbb{N}$, let $\hat{K}_{2,t}$ denote the $K_{2,t}$ 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 $P_1$ in the game $\mathcal{R}(K_{\aleph_0}, \hat{K}_{2,3})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{R}(K_{\aleph_0}, \hat{K}_{2,3})$ is a win for Player 1 Bowler, Nathan Ortmüller, Henri Combinatorics The Strong Ramsey game $\mathcal{R}(B,G)$ is a two player game with players $P_1$ and $P_2$, where $B$ and $G$ are $k$-uniform hypergraphs for some $k \geq 2$. $G$ is always finite, while $B$ may be infinite. $P_1$ and $P_2$ alternately color uncolored edges $e \in B$ in their respective color and $P_1$ 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 $t \in \mathbb{N}$, let $\hat{K}_{2,t}$ denote the $K_{2,t}$ 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 $P_1$ in the game $\mathcal{R}(K_{\aleph_0}, \hat{K}_{2,3})$. |
| title | $\mathcal{R}(K_{\aleph_0}, \hat{K}_{2,3})$ is a win for Player 1 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.03664 |