Ramsey number $R(7,12)$

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 $K_{12}$ in the second color.

Updates

• 2007 Upper bound: $6954$
  Huang Yi Ru, Wang Yuandi, Sheng Wancheng, Yang Jiansheng, Zhang Ke Min and Huang Jian, New Upper Bound Formulas with Parameters for Ramsey Numbers, Discrete Mathematics, 307 (2007) 760-763.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2011 Lower bound: $417$
  Xiaodong Xu, Zehui Shao and S.P. Radziszowski, More Constructive Lower Bounds on Classical Ramsey Numbers, SIAM Journal on Discrete Mathematics, 25 (2011) 394-400.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2020 Upper bound: $4665$
  V. Angeltveit and B.D. McKay, personal communication (2019-2024).
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]