Abstract
We study k-overlap-free binary infinite words that are binary infinite words which can contain only overlaps xyxyx with |x| ≤ k-1. We prove that no such word can be generated by morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist k-overlap-free binary infinite words which are not (k-1)-overlap-free. As an application, we prove that, for every integer n, there exists infinitely many k-overlap-free binary infinite partial words with n holes.