Diagonal Ramsey via effective quasirandomness
Ashwin Sah
Abstract
We improve the upper bound for diagonal Ramsey numbers to R(k+1,k+1)≤exp(−c(logk)2)2kk for k≥3. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal “effective quasirandomness” results about convergence of graphs. This optimality represents a natural barrier to improvement.
Topics & Concepts
DiagonalMathematicsRamsey's theoremCombinatoricsUpper and lower boundsConvergence (economics)Discrete mathematicsGeometryMathematical analysisGraphEconomicsEconomic growthLimits and Structures in Graph TheoryAdvanced Graph Theory ResearchAdvanced Topology and Set Theory