Graphs with m edges and no clique of size near sqrt(m) must have a cut exceeding m/2 by a power of m.
de Caen.Large equiangular sets of lines in Euclidean space.Electronic Journal of Combinatorics 7 (2000): #R55
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Beyond the MaxCut problem in $H$-free graphs
Graphs with m edges and no clique of size near sqrt(m) must have a cut exceeding m/2 by a power of m.