Upper bounds are found for the Ramsey function. We prove R(3, x) < cx2/lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1/(ln x)k − 2 asymptotically in x.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics