Given integers, we say that a graph is-free if there exists a red/blue edge coloring of such
that it contains neither a red nor a blue. Given a function, the Ramsey–Turán number is the …

We study the generalized Ramsey--Tur\'an function $\mathrm {RT}(n, K_s, K_t, o (n)) $,
which is the maximum possible number of copies of $ K_s $ in an $ n $-vertex $ K_t $-free …

Combining two classical notions in extremal combinatorics, the study of Ramsey-Tur\'an
theory seeks to determine, for integers $ m\le n $ and $ p\leq q $, the number $\mathsf {RT} …

Given integers $ p, q\ge2 $, we say that a graph $ G $ is $(K_p, K_q) $-free if there exists a
red/blue edge coloring of $ G $ such that it contains neither a red $ K_p $ nor a blue $ K_q …

Given graphs H_1,...,H_k, a graph G is (H_1,...,H_k)-free if there is a k-edge-coloring
ϕ:E(G)→k with no monochromatic copy of H_i with edges of color i for each i∈k. Fix a …

The Ramsey-Tur\'an problem for $ K_p $ asks for the maximum number of edges in an $ n $-
vertex $ K_p $-free graph with independence number $ o (n) $. In a natural generalization of …

In 1969, Erd\H {o} s and S\'{o} s initiated the study of the Ramsey-Tur\'{a} n type problems:
Determine the maximum number of edges of an $ n $-vertex $ K_ {p+ 1} $-free graph without …

The foundational result in extremal graph theory is Turán's theorem, which determines the
maximum number of edges in an n-vertex graph with no clique Kp as a subgraph. The …

Given graphs $ H_1,\ldots, H_k $, a graph $ G $ is $(H_1,\ldots, H_k) $-free if there is a $ k $-
edge-colouring $\phi: E (G)\rightarrow [k] $ with no monochromatic copy of $ H_i $ with …