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An extremal graph in which the forced triangles are all the same color. Call the number of red monochromatic forced triangles and
the number of blue monochromatic forced triangles, then a blue-empty graph is an extremal graph with
. For even
, a blue-empty graph can be achieved by coloring red two complete subgraphs of
points (the red net method). There is no blue-empty coloring for odd
except for
(Lorden 1962).
Lorden, G. "Blue-Empty Chromatic Graphs." Amer. Math. Monthly 69, 114-120, 1962.
Sauvé, L. "On Chromatic Graphs." Amer. Math. Monthly 68, 107-111, 1961.
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