Blue-Empty Graph

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).

REFERENCES

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.