Ramsey number $R(3,8)$

The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{3}$ in the first color or a monochromatic $K_{8}$ in the second color.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $28$ Checked construction
  ramsey-3-8-lower-28, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 1982 Lower bound: $28$
  C. Grinstead and S. Roberts, On the Ramsey Numbers R(3, 8) and R(3, 9), Journal of Combinatorial Theory, Series B, 33 (1982) 27-51.
  [via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]
• 1992 Upper bound: $28$
  B.D. McKay and Zhang Ke Min, The Value of the Ramsey Number R(3, 8), Journal of Graph Theory, 16 (1992) 99-105.
  [via Small Ramsey Numbers, Stanisław Radziszowski, revision #18, 2026-04-24]