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### Paper:

TR12-124 | 29th September 2012 02:48

#### A rank lower bound for cutting planes proofs of Ramsey Theorem

TR12-124
Authors: Massimo Lauria
Publication: 29th September 2012 03:17
Keywords:

Abstract:

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 $r(k,k)\leq 4^{k}$ requires cutting planes proof
of high rank. In order to do that we show a protection lemma which
could be of independent interest.

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