New lower bounds for the Ramsey numbers R(5,15) and R(8,12)
Year: 2026
Type: preprint
Abstract: We give a circulant two-colouring of the edges of K_278 with no red K_5 and no blue K_15, and a two-colouring of the edges of K_511 with no red K_8 and no blue K_12. Hence R(5,15) ≥ 279, improving the lower bound 275 recorded in Radziszowski's dynamic survey, and R(8,12) ≥ 512, improving the bound 511 from a colouring published in 2026. The first colouring was found by a tabu search over circulant colourings; the second adds one vertex to the published colouring and changes the colour of one of its edges. Every property was checked on the full graph by at least two programs written independently of each other. The colourings and checkers are at https://github.com/arhancanli/quantavane-ramsey-records.
Author: Canli, Arhan
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225046026