Independent sets and repeated degrees
We answer a question of Erdos, Faudree, Reid, Schelp and Staton by showing that for every integer k ≥ 2 there is a triangle-free graph G of order n such that no degree in G is repeated more than k times and ind(G) = (1 + o(1))n/k.
Bollobás, B., & Scott, A. (1997). Independent sets and repeated degrees. Discrete Mathematics, 170 (1-3), 41-49. https://doi.org/10.1016/0012-365X(95)00355-Z