We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on
The triangle‐free process begins with an empty graph on
- PAR ID:
- 10260116
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Random Structures & Algorithms
- Volume:
- 58
- Issue:
- 2
- ISSN:
- 1042-9832
- Page Range / eLocation ID:
- p. 221-293
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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n vertices, 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 <B such that (under optimal play) Proposer wins with high probability if, while Decider wins with high probability if . This is a factor of larger than the lower bound coming from the off‐diagonal Ramsey number r (3,s ). -
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