### Abstract

We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)^{2}/2 and (r + 1)^{2}α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).

Original language | English |
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Pages (from-to) | 63-69 |

Number of pages | 7 |

Journal | Journal of Graph Theory |

Volume | 13 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**Independence number, connectivity, and r‐factors.** / Nishimura, Tsuyoshi.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 13, no. 1, pp. 63-69. https://doi.org/10.1002/jgt.3190130109

}

TY - JOUR

T1 - Independence number, connectivity, and r‐factors

AU - Nishimura, Tsuyoshi

PY - 1989/1/1

Y1 - 1989/1/1

N2 - We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).

AB - We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).

UR - http://www.scopus.com/inward/record.url?scp=84986468529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986468529&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190130109

DO - 10.1002/jgt.3190130109

M3 - Article

AN - SCOPUS:84986468529

VL - 13

SP - 63

EP - 69

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -