### Abstract

For a graph H, the extremal number ex(n, H) is the maximum number of edges in a graph of order n not containing a subgraph isomorphic to H. Let δ(H)>0 and δ(H) denote the minimum degree and maximum degree of H, respectively. We prove that for all n sufficiently large, if H is any graph of order n with δ(H)≤n/40, then ex(n,H)=(n-12)+δ(H)-1. The condition on the maximum degree is tight up to a constant factor. This generalizes a classical result of Ore for the case H=C_{n}, and resolves, in a strong form, a conjecture of Glebov, Person, and Weps for the case of graphs. A counter-example to their more general conjecture concerning the extremal number of bounded degree spanning hypergraphs is also given.

Original language | English (US) |
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Pages (from-to) | 337-343 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 103 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2013 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Keywords

- Packing
- Spanning subgraph
- Turan number

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## Cite this

*Journal of Combinatorial Theory. Series B*,

*103*(3), 337-343. https://doi.org/10.1016/j.jctb.2013.02.002