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Title: Ramsey, Paper, Scissors

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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Award ID(s):
1855635
PAR ID:
10173272
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
57
Issue:
4
ISSN:
1042-9832
Page Range / eLocation ID:
p. 1157-1173
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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