Supersaturation for subgraph counts

Abstract

The classic extremal problem is that of computing the maximum number of edges in an $F$-free graph. In the case where $F=K_{r+1}$, the extremal number was determined by Turán. Later results, known as supersaturation theorems, proved that in a graph containing more edges than the extremal number, there must also be many copies of $K_{r+1}$. Alon and Shikhelman introduced a broader class of problems asking for the maximum number of copies of a graph $T$ in an $F$-free graph. In this paper, we determine some of these generalized extremal numbers and prove supersaturation results for them.

References in corpus (1)

• Maximizing five-cycles in $K_r$-free graphs

Cited by in corpus (4)

• Counting copies of a fixed subgraph in $F$-free graphs
• Every graph is eventually Turán-good
• Maximizing five-cycles in $K_r$-free graphs
• Paths of Length Three are $K_{r+1}$-Turán Good