The chromatic gap and its extremes
  The {\em chromatic gap} is the difference between the chromatic number and the clique number of a graph. Here we investigate $\gap(n)$, the maximum chromatic gap over graphs on $n$ vertices. Can the extremal graphs be explored? While computational problems related to the chromatic gap are hopeless, an interplay between Ramsey theory and matching theory leads to a simple and (almost) exact formula for $\gap(n)$ in terms of Ramsey numbers. 
Andr\'as Gy\'arf\'as, Andr\'as Seb\~o, Nicolas Trotignon
math.CO