The complexity of proving that a graph is Ramsey

0474390 - MÚ 2018 RIV HU eng J - Journal Article
Lauria, M. - Pudlák, Pavel - Rödl, V. - Thapen, Neil
The complexity of proving that a graph is Ramsey.
Combinatorica. Roč. 37, č. 2 (2017), s. 253-268. ISSN 0209-9683. E-ISSN 1439-6912
R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061
Institutional support: RVO:67985840
Keywords : complexity * c-Ramsey graphs
OECD category: Pure mathematics
Impact factor: 1.406, year: 2017
http://link.springer.com/article/10.1007%2Fs00493-015-3193-9

We say that a graph with n vertices is c-Ramsey if it does not contain either a clique or an independent set of size c log n. We define a CNF formula which expresses this property for a graph G. We show a superpolynomial lower bound on the length of resolution proofs that G is c-Ramsey, for every graph G. Our proof makes use of the fact that every c-Ramsey graph must contain a large subgraph with some properties typical for random graphs.
Permanent Link: http://hdl.handle.net/11104/0271451