Erdos-Selfridge Theorem for Nonmonotone CNFs
Abstract
In an influential paper, Erdos and Selfridge introduced the Maker-Breaker game played on a hypergraph, or equivalently, on a monotone CNF. The players take turns assigning values to variables of their choosing, and Breaker's goal is to satisfy the CNF, while Maker's goal is to falsify it. The Erdos-Selfridge Theorem says that the least number of clauses in any monotone CNF with k literals per clause where Maker has a winning strategy is Θ(2) q. We study the analogous question when the CNF is not necessarily monotone. We prove bounds of Θp √2 k q when Maker plays last, and ω(1.5) q and O(rk) q when Breaker plays last, where r = (1 +√5){2 ≈ 1.618 is the golden ratio.
Publication Title
Leibniz International Proceedings in Informatics, LIPIcs
Recommended Citation
Rahman, M., & Watson, T. (2022). Erdos-Selfridge Theorem for Nonmonotone CNFs. Leibniz International Proceedings in Informatics, LIPIcs, 227 https://doi.org/10.4230/LIPIcs.SWAT.2022.31
