Supersaturation strengthens an extremal existence theorem by forcing many copies of a forbidden graph when the edge count exceeds its extremal threshold by a fixed density. For a fixed clique, the Erdős-Stone theorem and averaging over bounded-size random vertex subsets give a positive multiple of copies.
Choose a fixed sample size for which the normalized Turan theorem bound lies below the given density by a positive margin. The expected edge count in a random -vertex subset then forces a positive proportion of subsets to contain a forbidden-size clique. Each clique belongs to a known number of subsets, so double counting gives a positive constant times cliques.
Articles by others on the same topic
Supersaturation is a state of a solution in which the concentration of a solute exceeds its solubility limit at a given temperature and pressure. Under normal conditions, a solution will achieve saturation when no more solute can dissolve in a solvent at that specific temperature and pressure. However, in a supersaturated solution, the dissolved solute exceeds this equilibrium concentration.