Blue-Empty Graph

An Extremal Graph in which the forced Triangles are all the same color. Call $R$ the number of red Monochromatic Forced Triangles and $B$ the number of blue Monochromatic Forced Triangles, then a blue-empty graph is an Extremal Graph with $B = 0$. For Even $n$, a blue-empty graph can be achieved by coloring red two Complete Subgraphs of $n/2$ points (the Red Net method). There is no blue-empty coloring for Odd $n$ except for $n=7$ (Lorden 1962).

See also Complete Graph, Extremal Graph, Monochromatic Forced Triangle, Red Net

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.