Hefetz, D. and Kusch, C. and Narins, L. and Pokrovskiy, Alexey and Requilé, C. and Sarid, A. (2017) Strong Ramsey games: drawing on an infinite board. Journal of Combinatorial Theory, Series A 150 , pp. 248-266. ISSN 0097-3165.
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Abstract
We consider the strong Ramsey-type game R(k)(H,ℵ0), played on the edge set of the infinite complete k-uniform hypergraph KkN. Two players, called FP (the first player) and SP (the second player), take turns claiming edges of K^k_N with the goal of building a copy of some finite predetermined k-uniform hypergraph H. The first player to build a copy of H wins. If no player has a strategy to ensure his win in finitely many moves, then the game is declared a draw. In this paper, we construct a 5-uniform hypergraph H such that R(5)(H,ℵ0) is a draw. This is in stark contrast to the corresponding finite game R(5)(H,n), played on the edge set of K5n. Indeed, using a classical game-theoretic argument known as \emph{strategy stealing} and a Ramsey-type argument, one can show that for every k-uniform hypergraph G, there exists an integer n0 such that FP has a winning strategy for R(k)(G,n) for every n≥n0.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 21 Jan 2019 11:11 |
| Last Modified: | 02 Aug 2023 17:47 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/25893 |
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