Localized versions of extremal problems

We generalize several classical theorems in extremal combi-natorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Turan's theorem, the Erdos-Gallai the-orem, the LYM-inequality, the Erdos-Ko-Rado theorem and the Erdos-Szekeres theorem on sequences. (c) 2023 Elsevier Ltd. All rights reserved.