A new proof of the Gan--Loh--Sudakov conjecture. (arXiv:2201.05181v1 [math.CO]) http://arxiv.org/abs/2201.05181
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 $n = a(Δ+1)+b \ (0 \le b \le Δ)$.
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