The Ramsey number R(G,H) of two graphs G and H is the smallest integer r such that every graph F with at least r vertices contains G as a subgraph, or the complement of F contains H as a subgraph. A graph which does not contain G and whose complement does not contain H is called a Ramsey graph for (G,H).
This page contains all Ramsey numbers R(K3,G) for graphs of order 10. More information about how these Ramsey numbers were computed can be found in [1]. All Ramsey graphs which were constructed in [1] can be downloaded from the searchable database of graphs by searching for the keywords 'ramsey * order 10'.
For a good overview of the results and bounds of Ramsey numbers which are currently known, see Radziszowski's dynamic survey [2].
More lists of Ramsey graphs can be found at:
All graph lists on this page are currently only available in 'graph6' format. The larger files are compressed with gzip.
There are 10 graphs with Ramsey number R(K3,G) > 30 for which we were unable to determine their Ramsey number. They can be downloaded here. More information about these graphs can be found in [1].
Ramsey number | Number of graphs |
---|---|
19 | 10101711 |
20 | 504 |
21 | 1602240 |
22 | 3155 |
23 | 6960 |
24 | 0 |
25 | 1384 |
26 | 316 |
27 | 92 |
28 | 142 |
29 | 30 |
30 | 3 |
31 | 16 + ? |
36 | 8 + ? |
Ramsey number | Number of graphs |
---|---|
10 | 151 |
11 | 596 |
12 | 168 |
13 | 3734 |
14 | 447 |
15 | 18048 |
16 | 2933 |
17 | 243856 |
18 | 16301 |
19 | 311 |
20 | 0 |
21 | 1869 |
22 | 22 |
23 | 114 |
24 | 0 |
25 | 28 |
26 | 5 |
27 | 3 |
28 | 9 |
31 | 1 |
36 | 1 |
[1] G. Brinkmann, J. Goedgebeur and J.C. Schlage-Puchta, Ramsey numbers R(K3,G) for graphs of order 10, Electronic Journal of Combinatorics, 19(4), 2012.
[2] S.P. Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics , Dynamic Survey 1, revision 13, 2011.