Let $f(n)$ be a positive function and $H$ a graph. Denote by $\textbf{RT}(n,H,f(n))$ the maximum number of edges of an $H$-free graph on $n$ vertices with independence number less than $f(n)$. It is shown that $\textbf{RT}(n,K_4+mK_1,o(\sqrt{n\log n}))=o(n^2)$ for any fixed integer $m\geqslant 1$ and $\textbf{RT}(n,C_{2m+1},f(n))=O(f^2(n))$ for any fixed integer $m\geqslant 2$ as $n\to\infty$.
@article{10_37236_9135,
author = {Meng Liu and Yusheng Li},
title = {Two results on {Ramsey-Tur\'an} theory},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/9135},
zbl = {1476.05134},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9135/}
}
TY - JOUR
AU - Meng Liu
AU - Yusheng Li
TI - Two results on Ramsey-Turán theory
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9135/
DO - 10.37236/9135
ID - 10_37236_9135
ER -
%0 Journal Article
%A Meng Liu
%A Yusheng Li
%T Two results on Ramsey-Turán theory
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9135/
%R 10.37236/9135
%F 10_37236_9135
Meng Liu; Yusheng Li. Two results on Ramsey-Turán theory. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/9135
