Localized versions of extremal problems
Combinatorics
2022-05-30 v2
Abstract
We generalize several classical theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Tur\'an's theorem, the Erd\H{o}s-Gallai theorem, the LYM-inequality, the Erd\H{o}s-Ko-Rado theorem and the Erd\H{o}s-Szekeres theorem on sequences.
Cite
@article{arxiv.2205.12246,
title = {Localized versions of extremal problems},
author = {David Malec and Casey Tompkins},
journal= {arXiv preprint arXiv:2205.12246},
year = {2022}
}
Comments
Fixed a typo in statement of Theorem 2