Use of MAX-CUT for Ramsey Arrowing of Triangles

  title={Use of MAX-CUT for Ramsey Arrowing of Triangles},
  author={Alexander Lange and Stanislaw P. Radziszowski and Xiaodong Xu},
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
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  • Paul Erdős, András Hajnal
  • Journal of Combinatorial Theory,
  • 1967
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  • Marcus Schaefer
  • Geombinatorics
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