English

A Note on Tur\'an Numbers and the Erd\H{o}s-Stone-Simonovits Theorem

Combinatorics 2025-10-02 v1

Abstract

Given a fixed graph H, we say that a graph G is H-free if G does not contain H as a subgraph. The Tur\'an number ex(n, H) of H is the maximum number of edges in an n-vertex H-free graph. The study of Tur\'an number of graphs is a central topic in extremal graph theory. The purpose of this article is to present some well-known results about this field but also to prove the Erd\H{o}s-Stone-Simonovits theorem in an original manner.

Keywords

Cite

@article{arxiv.2510.00338,
  title  = {A Note on Tur\'an Numbers and the Erd\H{o}s-Stone-Simonovits Theorem},
  author = {Stefan Gobej},
  journal= {arXiv preprint arXiv:2510.00338},
  year   = {2025}
}

Comments

8 pages, no figures