@article{Lange2012UseOM,
title={Use of MAX-CUT for Ramsey Arrowing of Triangles},
author={Alexander Lange and Stanislaw P. Radziszowski and Xiaodong Xu},
journal={CoRR},
year={2012},
volume={abs/1207.3750}
}

In 1967, Erdős and Hajnal asked the question: Does there exist a K4-free graph that is not the union of two triangle-free graphs? Finding such a graph involves solving a special case of the classical Ramsey arrowing operation. Folkman proved the existence of these graphs in 1970, and they are now called Folkman graphs. Erdős offered $100 for deciding if one exists with less than 10 vertices. This problem remained open until 1988 when Spencer, in a seminal paper using probabilistic techniques… CONTINUE READING