Ramsey number $R(6,8)$

The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{6}$ in the first color or a monochromatic $K_{8}$ in the second color.

Updates

• 1994 Upper bound: $495$
  J. Mackey, Combinatorial Remedies, Ph.D. thesis, Department of Mathematics, University of Hawaii, 1994.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2015 Lower bound: $134$
  G. Exoo and M. Tatarevic, New Lower Bounds for 28 Classical Ramsey Numbers, Electronic Journal of Combinatorics, http:// www.combinatorics.org, #P3.11, 22(3) (2015), 12 pages. Graphs available at the journal site and at http://cs.indstate.edu/ge/RAMSEY/ExTa.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2020 Upper bound: $423$
  V. Angeltveit and B.D. McKay, personal communication (2019-2024).
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]