Maker playing against an invisible Breaker
Combinatorics
2025-07-31 v1
Abstract
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 Maker-PhantomBreaker games where the board is the edge set of the complete graph on vertices, , 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- game and Hamiltonicity game. In particular, we focus on characterizing all biases for which Maker wins asymptotically almost surely.
Cite
@article{arxiv.2507.22519,
title = {Maker playing against an invisible Breaker},
author = {Dennis Clemens and Fabian Hamann and Mirjana Mikalački and Yannick Mogge and Miloš Stojaković},
journal= {arXiv preprint arXiv:2507.22519},
year = {2025}
}