## Intersections of hypergraphs

- Béla Bollobás, Alex D. Scott
- J. Comb. Theory, Ser. B
- 2015

3 Excerpts

- Published 2003 in Combinatorics, Probability & Computing

A celebrated theorem of Turán asserts that every graph on n vertices with more than r− 1 2r n 2 edges contains a copy of a complete graph Kr+1. In this paper we consider the following more general question. Let G be a Kr+1-free graph of order n and let α be a constant, 0 < α 1. How dense can every induced subgraph of G on αn vertices be? We prove the following local density extension of Turán’s theorem. For every integer r 2 there exists a constant cr < 1 such that, if cr α 1 and every αn vertices of G span more than r− 1 2r (2α− 1)n

@article{Keevash2003LocalDI,
title={Local Density In Graphs With Forbidden Subgraphs},
author={Peter Keevash and Benny Sudakov},
journal={Combinatorics, Probability & Computing},
year={2003},
volume={12},
pages={139-153}
}