The chromatic threshold δχ (H) of a graph H is the infimum of d> 0 such that there exists C=
C (H, d) for which every H-free graph G with minimum degree at least d| G| satisfies χ (G)⩽ …

The celebrated Andr\'{a} sfai--Erd\H {o} s--S\'{o} s Theorem from 1974 shows that every $ n $-
vertex triangle-free graph with minimum degree greater than $2 n/5$ must be bipartite. Its …

Hypergraph Turán Problem: Some Open Questions Page 1 Hypergraph Turán Problem: Some
Open Questions Dhruv Mubayi, Oleg Pikhurko, Benny Sudakov October 10, 2011 1 Introduction …

The celebrated Andr\'{a} sfai--Erd\H {o} s--S\'{o} s Theorem from 1974 shows that every $ n $-
vertex triangle-free graph with minimum degree greater than $2 n/5$ must be bipartite. We …

Given two $ r $-uniform hypergraphs $ F $ and $ H $, we say that $ H $ has an $ F $-
covering if every vertex in $ H $ is contained in a copy of $ F $. Let $ c_ {i}(n, F) $ be the …

A classical result in extremal graph theory is Mantel's Theorem, which states that every
maximum triangle‐free subgraph of Kn is bipartite. A sparse version of Mantel's Theorem is …

Let H be an r-uniform hypergraph with r≥ 2 and let α (H) be its vertex independence
number. In the paper bounds of α (H) are given for different uniform hypergraphs: if H has no …

One of the earliest results in Extremal Combinatorics is Mantel's theorem from 1907 which
says that the largest triangle-free graph on a given number of vertices is the complete …

We study problems in extremal combinatorics with respect to forbidden induced subgraphs,
forbidden colored subgraphs, and forbidden subgraphs. In Chapter 2, we determine exactly …

Let F be an r-uniform hypergraph. The chromatic threshold of the family of F-free, r-uniform
hypergraphs is the infimum of all non-negative reals c such that the subfamily of F-free, r …