### Abstract

We give a strengthening of the closure concept for claw-free graphs introduced by the second author in 1997. The new closure of a claw-free graph $G$ defined here is uniquely determined and preserves the value of the circumference of $G$. We present an infinite family of graphs with $n$ vertices and $3n/2 -1$ edges for which the new closure is the complete graph $K_n$

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 13 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 2000 |

### Publication series

Name | Memorandum / Faculty of Mathematical Sciences |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1512 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C45
- MSC-05C35
- METIS-141182
- EWI-3332
- IR-65700

## Cite this

Broersma, H. J., & Ryjacek, Z. (2000).

*Strengthening the closure concept in claw-free graphs*. (Memorandum / Faculty of Mathematical Sciences; No. 1512). Enschede: Universiteit Twente.