### Abstract

Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (^{k}_{2}) - 1 is the famous result of Turán.

Original language | English |
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Pages (from-to) | 185-207 |

Number of pages | 23 |

Journal | Journal of Graph Theory |

Volume | 29 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1998 |

### Keywords

- Dirac's Theorem
- Extremal graphs
- Turán's Theorem

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Griggs, J. R., Simonovits, M., & Thomas, G. R. (1998). Extremal Graphs with Bounded Densities of Small Subgraphs.

*Journal of Graph Theory*,*29*(3), 185-207. https://doi.org/10.1002/(SICI)1097-0118(199811)29:3<185::AID-JGT6>3.0.CO;2-M