### 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 |
---|---|

Pages (from-to) | 49-55 |

Number of pages | 7 |

Journal | Australasian Journal of Combinatorics |

Volume | 21 |

Publication status | Published - 2000 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Australasian Journal of Combinatorics*,

*21*, 49-55.

**A recursive theorem on matching extension.** / Chan, Chi I.; Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - A recursive theorem on matching extension

AU - Chan, Chi I.

AU - Nishimura, Tsuyoshi

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84885905951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885905951&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 49

EP - 55

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

ER -