Ramsey number $R(7,8)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{7}$ in the first color or a monochromatic $K_{8}$ in the second color.
Lower bound:
$219$
Upper bound:
$832$
Updates
-
1993
Upper bound: $1031$
Huang Yi Ru and Zhang Ke Min, A New Upper Bound Formula on Ramsey Numbers, Journal of Shanghai University, Natural Science, 7 (1993) 1-3.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Lower bound: $219$
M. Tatarevic, personal communication, graph constructions for lower bounds on Ramsey numbers at http://github.com/milostatarevic/ramsey-numbers/tree/master/graphs (2020).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $832$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]