Survey of generalized Turán problems -- counting subgraphs

Abstract

For fixed graphs $H$ and $F$, the \emph{generalized Turán number} $\mathrm{ex}(n,H,F)$ is the maximum possible number of copies of a subgraph $H$ in an $n$-vertex $F$-free graph. This article is a survey of this extremal function whose study was initiated in an influential 2016 article by Alon and Shikhelman (\emph{J. Combin. Theory, B}, {\bf 121}, 2016).

arXiv commentWe welcome comments from the community, including suggested references. We especially encourage you to share any generalized Turán open problems to be included in Section 6!