A Rank Lower Bound for Cutting Planes Proofs of Ramsey's Theorem

Massimo Lauria
2016 ACM Transactions on Computation Theory  
Ramsey's Theorem is a cornerstone of combinatorics and logic. In its simplest formulation it says that there is a function r such that any simple graph with r(k, s) vertices contains either a clique of size k or an independent set of size s. We study the complexity of proving upper bounds for the number r(k, k). In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k, k) ≤ 4 k " requires cutting planes proof of high rank. In order to do that
more » ... show a protection lemma which could be of independent interest.
doi:10.1145/2903266 fatcat:aikdisyslzflboe65jqgi6p4l4