English

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.

Keywords

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

R2 v1 2026-06-24T11:27:26.103Z