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Ramsey number lower bounds
Colour 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.
Stanisław Radziszowski's dynamic survey Small Ramsey Numbers is the standard reference for the known bounds. Our colourings are public with a checker written in C.
2 sent to its maintainer.
Two Ramsey bounds
| Entry | Ours | Previous best | Status |
|---|---|---|---|
| R(5,15) ≥ 279 | 279 | 275 | sent |
| R(8,12) ≥ 512 | 512 | 511 | sent |
Questions
What does R(5,15) ≥ 279 mean?
That some red-blue colouring of the lines between 278 points has no 5 points joined all in red and no 15 points joined all in blue, so 279 points are needed to force one of them.
Are the exact values known?
No. For these parameters only lower and upper bounds are known; better colourings raise the lower bound.
Where can I check the colourings?
In github.com/arhancanli/quantavane-ramsey-records, with check.c, which searches the whole colouring for both kinds of group.