New lower bounds for the Ramsey numbers R(5,15) and R(8,12)

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23857056
Primary Topic
Limits and Structures in Graph Theory
Type
preprint
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preprint

New lower bounds for the Ramsey numbers R(5,15) and R(8,12)

Arhan Canli
Zenodo (CERN European Organization for Nuclear Research)
Limits and Structures in Graph Theory
preprint

New lower bounds for the Ramsey numbers R(5,15) and R(8,12)

Arhan Canli
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Limits and Structures in Graph Theory
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