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

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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.

Referenced on Wolfram|Alpha

Blue-Empty Graph

Cite this as:

Weisstein, Eric W. "Blue-Empty Graph." From MathWorld--A Wolfram Web Resource.

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