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).

# Blue-Empty Graph

## See also

Complete Graph, Extremal Graph, Monochromatic Forced Triangle, Red Net## Explore with Wolfram|Alpha

## 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.

## Referenced on Wolfram|Alpha

Blue-Empty Graph## Cite this as:

Weisstein, Eric W. "Blue-Empty Graph."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Blue-EmptyGraph.html