### Abstract

A graph G is called H-saturated if it does not contain any copy of H, but for any edge e in the complement of G, the graph G+e contains some H. The minimum size of an n-vertex H-saturated graph is denoted by sat(n,H). We prove sat(n,Ck)=n+n/k+O((n/k2)+k2)holds for all n≥k≥3, where Ck is a cycle with length k. A graph G is H-semisaturated if G+e contains more copies of H than G does for â̂€eâ̂̂E(Ḡ). Let ssat (n,H) be the minimum size of an n-vertex H-semisaturated graph. We have ssat(n,Ck)=n+n/(2k)+O((n/k2)+k).We conjecture that our constructions are optimal for n>n0(k).

Original language | English |
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Pages (from-to) | 203-215 |

Number of pages | 13 |

Journal | Journal of Graph Theory |

Volume | 73 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2013 |

### Keywords

- cycles
- extremal graphs
- graphs
- minimal saturated graphs

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Füredi, Z., & Kim, Y. (2013). Cycle-saturated graphs with minimum number of edges.

*Journal of Graph Theory*,*73*(2), 203-215. https://doi.org/10.1002/jgt.21668