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Maker playing against an invisible Breaker
Citation Link: https://doi.org/10.15480/882.16098
Publikationstyp
Preprint
Date Issued
2025-07-30
Sprache
English
TORE-DOI
We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased a : b Maker-PhantomBreaker games where the board is the edge set of the complete graph on n vertices, Kn, and Maker has no information about PhantomBreaker’s choices of edges. We give randomized strategies for both players in four classical games: connectivity game, perfect matching game, mindegree-k game and Hamiltonicity game. In particular, we focus on characterizing all biases pa : bq for which Maker wins asymptotically almost surely.
DDC Class
510: Mathematics
Publication version
submittedVersion
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2507.22519v1.pdf
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614.95 KB
Format
Adobe PDF