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:

- Minimal Ramsey graphs
- Ramsey graphs (Brendan McKay)
- Ramsey constructions (Geoffrey Exoo)

All graph lists on this page are currently only available in 'graph6' format. The larger files are compressed with gzip.

Ramsey | Number of |
---|---|

number | 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 + ? |

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 |

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.