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We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph onnvertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at leasts. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants 0 < A < Bsuch that (under optimal play) Proposer wins with high probability if, while Decider wins with high probability if. This is a factor oflarger than the lower bound coming from the off‐diagonal Ramsey numberr(3,s).
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This content will become publicly available on March 1, 2026
On the Constructor–Blocker game
Abstract In the Constructor–Blocker game, two players, Constructor and Blocker, alternately claim unclaimed edges of the complete graph . For given graphs and , Constructor can only claim edges that leave her graph ‐free, while Blocker has no restrictions. Constructor's goal is to build as many copies of as she can, while Blocker attempts to minimize the number of copies of in Constructor's graph. The game ends once there are no more edges that Constructor can claim. The score of the game is the number of copies of in Constructor's graph at the end of the game when both players play optimally and Constructor plays first. In this paper, we extend results of Patkós, Stojaković and Vizer on to many pairs of and : We determine when and , also when both and are odd cycles, using Szemerédi's Regularity Lemma. We also obtain bounds of when and .
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- Award ID(s):
- 2152488
- PAR ID:
- 10596998
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Graph Theory
- Volume:
- 108
- Issue:
- 3
- ISSN:
- 0364-9024
- Page Range / eLocation ID:
- 492 to 507
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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