We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $\Delta$ has no more than $a\binom{\Delta+1}{t}+\binom{b}{t}$ cliques of size $t \ (t \ge 3)$, where $n = a(\Delta+1)+b \ (0 \le b \le \Delta)$.
@article{10_37236_10972,
author = {Ting-Wei Chao and Zichao Dong},
title = {A simple proof of the {Gan-Loh-Sudakov} conjecture},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10972},
zbl = {1498.05203},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10972/}
}
TY - JOUR
AU - Ting-Wei Chao
AU - Zichao Dong
TI - A simple proof of the Gan-Loh-Sudakov conjecture
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10972/
DO - 10.37236/10972
ID - 10_37236_10972
ER -
%0 Journal Article
%A Ting-Wei Chao
%A Zichao Dong
%T A simple proof of the Gan-Loh-Sudakov conjecture
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10972/
%R 10.37236/10972
%F 10_37236_10972
Ting-Wei Chao; Zichao Dong. A simple proof of the Gan-Loh-Sudakov conjecture. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10972
