Survey of generalized Tur\'an problems -- counting subgraphs

Dániel Gerbner; Cory Palmer

Survey of generalized Tur\'an problems -- counting subgraphs

Combinatorics 2025-06-05 v1

Authors: Dániel Gerbner , Cory Palmer

Abstract

For fixed graphs $H$ and $F$ , the \emph{generalized Tur\'an 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).

Keywords

turán theory graph theory random graphs

Cite

@article{arxiv.2506.03418,
  title  = {Survey of generalized Tur\'an problems -- counting subgraphs},
  author = {Dániel Gerbner and Cory Palmer},
  journal= {arXiv preprint arXiv:2506.03418},
  year   = {2025}
}

Comments

We welcome comments from the community, including suggested references. We especially encourage you to share any generalized Tur\'an open problems to be included in Section 6!

Survey of generalized Tur\'an problems -- counting subgraphs

Abstract

Keywords

Cite

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