All Questions

Fix a positive integer $r$ and real $\delta \in (0,1)$. Let $G$ be an undirected graph on $n$ vertices. Suppose that $G$ does not contain an $r$-regular subgraph on at least $\delta n$ vertices (i.e., ...

Define $$RT(n,K_l,f(n))=ex_l(n,f(n))=\max_G\{e(G): K_l \not\subset G, v(G)=n, \alpha(G)\leq f(n)\}$$ and the Ramsey-Turán density function $f_l:(0,1] \to \mathbb{R}$ as $$f_l(\alpha)=\lim_{n\to \infty}...

Liven large enough $k\in\Bbb N$ fix $m\in\{2,3,\dots,k\}$ and fix $4k$ cardinality set $K_{4k}$. What is the maximum $n\in\Bbb N$ such that at some $t\geq2n-1$ there are $$\mbox{ subsets }L_1,L_2,\...