## Abstract

The classical extremal problem is that of computing the maximum number of edges in an F-free graph. In particular, Turán’s theorem entirely resolves the case where F= K_{r}_{+}_{1}. 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 extremal problems, asking for the maximum number of copies of a graph T in an F-free graph (so that T= K_{2} is the classical extremal number). In this paper we determine some of these generalized extremal numbers when T and F are stars or cliques and prove some supersaturation results for them.

Original language | English |
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Article number | 65 |

Journal | Graphs and Combinatorics |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2022 |

## Keywords

- Extremal graph theory
- Generalized Turán problem
- Supersaturation