Ramsey numbers

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.

Ramsey numbers R(K3,G) for connected graphs of order 10

Ramsey Number of
number graphs
1910101711
20504
211602240
223155
236960
240
251384
26316
2792
28142
2930
303
3116 + ?
368 + ?

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 of
number graphs
10151
11596
12168
133734
14447
1518048
162933
17243856
1816301
19311
200
211869
2222
23114
240
2528
265
273
289
311
361

References

[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.