A simple proof of the Gan-Loh-Sudakov conjecture (Q2088706)

Summary: 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 \(t\) \((t \geqslant 3)\), where \(n = a(\Delta+1)+b\) \((0 \leqslant b \leqslant \Delta)\).