The number of monochromatic forced triangles is the minimum number of triangles whose three edges have the same color in a two-coloring
of the edges of a complete
graph. For , this minimum is
(1)
For ,
2, ..., the first few minimum numbers of monochromatic forced triangles are 0, 0,
0, 0, 0, 2, 4, 8, 12, 20, 28, 40, ... (OEIS A014557).
Goodman, A. W. "On Sets of Acquaintances and Strangers at Any Party." Amer. Math. Monthly66, 778-783, 1959.Sloane,
N. J. A. Sequence A014557 in "The
On-Line Encyclopedia of Integer Sequences."
, this minimum is
,
2, ..., the first few minimum numbers of monochromatic forced triangles are 0, 0,
0, 0, 0, 2, 4, 8, 12, 20, 28, 40, ... (OEIS A014557).
