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

Massimo Lauria
2013 Lecture Notes in Computer Science  
Ramsey 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 we
more » ... how a protection lemma which could be of independent interest.
doi:10.1007/978-3-642-39071-5_26 fatcat:tb624rsot5dtbi56vwgstndnku