Monochromatic Forced Triangle

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least

 {1/3u(u-1)(u-2)   for n=2u; 2/3u(u-1)(4u+1)   for n=4u+1; 2/3u(u+1)(4u-1)   for n=4u+3.

The first few numbers of monochromatic forced triangles are 0, 0, 0, 0, 0, 2, 4, 8, 12, 20, 28, 40, ... (OEIS A014557).

See also

Complete Graph, Extremal Graph

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Goodman, A. W. "On Sets of Acquaintances and Strangers at Any Party." Amer. Math. Monthly 66, 778-783, 1959.Sloane, N. J. A. Sequence A014557 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Monochromatic Forced Triangle

Cite this as:

Weisstein, Eric W. "Monochromatic Forced Triangle." From MathWorld--A Wolfram Web Resource.

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