Ramsey number $R(3,12)$

The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{3}$ in the first color or a monochromatic $K_{12}$ in the second color.

Updates

• 2001 Upper bound: $59$
  A. Lesser, Theoretical and Computational Aspects of Ramsey Theory, Examensarbeten i Matematik, Matematiska Institutionen, Stockholms Universitet, 3, http://www2.math.su.se/gemensamt/grund/exjobb/matte/2001 (2001).
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2015 Lower bound: $53$
  M. Kolodyazhny, Novye Nizhnie Granitsy Chisel Ramseya R(3, 12) i R(3, 13) (in Russian), Matematicheskoye i Informacionnoe Modelirovanie, Tyumen, 14 (2015) 126-130.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]