### Abstract

A graph G having a perfect matching (or I-factor) is called n-fextendable if every matching of size n is extended to a I-factor. Further, G is said to be 〈r: m, n 〉-extendable if, for every connected subgraph S of order 2r for which G \ V(S) is connected, S is m-extendable and G \ V(S) is nextendable. We prove the following: Let p, r, m, and n be positive integers with p - r > nand r > m. Then every 2-connected 〈r: m, n〉-extendable graph of order 2p is 〈r + 1: m + 1, n - 1〉-extendable.

Original language | English |
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Pages (from-to) | 49-55 |

Number of pages | 7 |

Journal | Australasian Journal of Combinatorics |

Volume | 21 |

Publication status | Published - 2000 Dec 1 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Chan, C. I., & Nishimura, T. (2000). A recursive theorem on matching extension.

*Australasian Journal of Combinatorics*,*21*, 49-55.