Ramsey number $R(5,7)$
The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{5}$ in the first color or a monochromatic $K_{7}$ in the second color.
Lower bound:
$80$
Upper bound:
$133$
Updates
-
1993
Upper bound: $143$
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] -
1997
Lower bound: $80$
N.J. Calkin, P. Erdős and C.A. Tovey, New Ramsey Bounds from Cyclic Graphs of Prime Order, SIAM Journal on Discrete Mathematics, 10 (1997) 381-387.
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06] -
2020
Upper bound: $133$
V. Angeltveit and B.D. McKay, personal communication (2019-2024).
[via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]