Supersaturation Problem for Color-Critical Graphs
Zelealem Yilma, LIAFA

We call a graph on n vertices F-supersaturated if it contains more than ex(n,F) (the Turán number) of edges. We investigate the function h(F,n,q), the minimum number of copies of F that an F-supersaturated graph with exactly ex(n,F)+q edges can have. We determine h(F,n,q) asymptotically when F is color-critical (that is, it contains an edge whose deletion reduces the chromatic number) and q=o(n^2).