Supersaturation beyond color-critical graphs

A classic result of Rademacher from 1941 led to the study of supersaturation problems of graphs, which aim to count the minimum number of copies of a given graph F among all graphs with n vertices and m edges. This is closely related to a central concept in Extremal Graph Theory -- the Turán number of F. Famous results of Erdös, and
Lovász and Simonovits determine the minimum number of cliques K_r in graphs whose number of edges exceed the Turán number of K_r by a linear term O(n). Subsequent works of Mubayi as well as Pikhurko and
Yilma extend these classical results from cliques to color-critical graphs, a rich family playing important roles in extremal problems. In this talk, we will discuss supersaturation problems beyond color-critical graphs and investigate natural enumerative parameters. Our results go beyond the previous results and show that supersaturation problems for general graphs can be rather complicate. Among others, we disprove a conjecture of Mubayi.

Bio
http://staff.ustc.edu.cn/~jiema/