A simple proof of the Gan-Loh-Sudakov conjecture

Abstract

We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $Δ$ has no more than $a\binom{Δ+1}{t}+\binom{b}{t}$ cliques of size $t \ (t \ge 3)$, where $n = a(Δ+1)+b \ (0 \le b \le Δ)$.