# A recursive theorem on matching extension

Chi I. Chan, Tsuyoshi Nishimura

Research output: Contribution to journalArticle

### 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 49-55 7 Australasian Journal of Combinatorics 21 Published - 2000

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics

### Cite this

In: Australasian Journal of Combinatorics, Vol. 21, 2000, p. 49-55.

Research output: Contribution to journalArticle

@article{75369cb9d5754f25a04a3f7c6402f058,
title = "A recursive theorem on matching extension",
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.",
author = "Chan, {Chi I.} and Tsuyoshi Nishimura",
year = "2000",
language = "English",
volume = "21",
pages = "49--55",
journal = "Australasian Journal of Combinatorics",
issn = "1034-4942",
publisher = "University of Queensland Press",

}

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

AN - SCOPUS:84885905951

VL - 21

SP - 49

EP - 55

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

ER -