A General Framework for Studying Finite Rainbow Configurations
Given a coloring of a set, classical Ramsey theory looks for various configurations within a color class. Rainbow configurations, also called anti-Ramsey configurations, are configurations that occur across distinct color classes. We present some very general results about the types of colorings that will guarantee various types of rainbow configurations in finite settings, as well as several illustrative corollaries. The main goal of this note is to present a flexible framework for decomposing finite sets while guaranteeing the existence of some desired structure across the decomposition.
Desgrottes, Mike; Senger, Steven; Soukup, David; and Zhu, Renjun, "A General Framework for Studying Finite Rainbow Configurations" (2020). Articles by College of Natural and Applied Sciences Faculty. 1644.
Springer Proceedings in Mathematics and Statistics