### Abstract

In this paper we consider graphs which have no k vertex-disjoint cycles. For given integers k, α let f (k, α) be the maximum order of a graph G with independence number α (G) ≤ α, which has no k vertex-disjoint cycles. We prove that f (k, α) = 3 k + 2 α - 3 if 1 ≤ α ≤ 5 or 1 ≤ k ≤ 2, and f (k, α) ≥ 3 k + 2 α - 3 in general. We also prove the following results: (1) there exists a constant c_{α} (depending only on α) such that f (k, α) ≤ 3 k + c_{α}, (2) there exists a constant t_{k} (depending only on k) such that f (k, α) ≤ 2 α + t_{k}, and (3) there exists no absolute constant c such that f (k, α) ≤ c (k + α).

Original language | English |
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Pages (from-to) | 1493-1498 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 307 |

Issue number | 11-12 |

DOIs | |

Publication status | Published - 2007 May 28 |

### Keywords

- Independence number
- Vertex-disjoint cycles

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Egawa, Y., Enomoto, H., Jendrol, S., Ota, K., & Schiermeyer, I. (2007). Independence number and vertex-disjoint cycles.

*Discrete Mathematics*,*307*(11-12), 1493-1498. https://doi.org/10.1016/j.disc.2005.11.086