Ramsey numbers
R(8,12) ≥ 512
R(8,12) is at least 512: Quantavane found a red-blue colouring of the lines between 511 points with no 8 points joined all in red and no 12 points joined all in blue. The best lower bound known before was 511.
Sent to Stanisław Radziszowski, who maintains the survey, on 26 October 2026.
The record
| Ours | R(8,12) ≥ 512 |
|---|---|
| Previous best | R(8,12) ≥ 511 |
| Previous source | a colouring of 510 points published in 2026 (Google's ramsey_number_bounds repository) |
| Found | 25 October 2026 |
| Status | Sent to Stanisław Radziszowski, who maintains the survey, on 26 October 2026. |
| Check | Two separate programs checked the full colouring: no red group of 8 and no blue group of 12. |
So among any 511 points the colouring can avoid both, and at least 512 points are needed to force a red group of 8 or a blue group of 12. The exact value of R(8,12) is unknown.
How it was found and checked
One vertex added to the published colouring of 510 points, with one of its edges recoloured. Two separate programs checked the full colouring: no red group of 8 and no blue group of 12.
git clone https://github.com/arhancanli/quantavane-ramsey-records
cd quantavane-ramsey-records
cc -O2 -o check check.c
./check colourings/R8_12_K511.txtColour every line between n points red or blue. The Ramsey number R(s,t) is the smallest n for which every colouring has s points joined all in red or t points joined all in blue. Most values are unknown. A colouring of n points with neither shows R(s,t) is at least n + 1.
Questions
What is the best known lower bound for R(8,12)?
512, from our colouring of 511 points; before it, 511 (a colouring of 510 points published in 2026 (Google's ramsey_number_bounds repository)).
Is the exact value of R(8,12) known?
No. Only lower and upper bounds are known.
Where is the colouring?
In the public repository, https://github.com/arhancanli/quantavane-ramsey-records/blob/main/colourings/R8_12_K511.txt.