On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions

Abstract

We investigate the distributions of the number of: (1) monochromatic complete subgraphs over edgewise 2-colorings of complete graphs; and (2) monochromatic arithmetic progressions over 2-colorings of intervals, as statistical Ramsey theory questions. We present convincing evidence that both distributions are very well-approximated by the Delaporte distribution.

Keywords:

• Ramsey’s theorem
• Van der Waerden’s theorem
• monochromatic subgraphs
• monochromatic arithmetic progressions
• Delaporte distribution

Notes

1 Available at http://www.aaronrobertson.org.

2 Available at http://www.aaronrobertson.org.