### Abstract

Let G be a graph, and let g and f be two integer-valued functions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G). A graph G is called a (g, f, n)-critical graph if G - N has a (g, f)-factor for each N ⊆ V(G) with |N| = n. In this paper, a necessary and sufficient condition for a graph to be (g, f, n)-critical is given. Furthermore, the properties of (g, f, n)-critical graph are studied.

Original language | English |
---|---|

Pages (from-to) | 71-82 |

Number of pages | 12 |

Journal | Ars Combinatoria |

Volume | 78 |

Publication status | Published - 2006 Jan |

Externally published | Yes |

### Keywords

- (g, f)-factor
- Factor-critical graph

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On (g, f, n)-critical graphs.** / Li, Jianxiang; Matsuda, Haruhide.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On (g, f, n)-critical graphs

AU - Li, Jianxiang

AU - Matsuda, Haruhide

PY - 2006/1

Y1 - 2006/1

N2 - Let G be a graph, and let g and f be two integer-valued functions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G). A graph G is called a (g, f, n)-critical graph if G - N has a (g, f)-factor for each N ⊆ V(G) with |N| = n. In this paper, a necessary and sufficient condition for a graph to be (g, f, n)-critical is given. Furthermore, the properties of (g, f, n)-critical graph are studied.

AB - Let G be a graph, and let g and f be two integer-valued functions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G). A graph G is called a (g, f, n)-critical graph if G - N has a (g, f)-factor for each N ⊆ V(G) with |N| = n. In this paper, a necessary and sufficient condition for a graph to be (g, f, n)-critical is given. Furthermore, the properties of (g, f, n)-critical graph are studied.

KW - (g, f)-factor

KW - Factor-critical graph

UR - http://www.scopus.com/inward/record.url?scp=33644693977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644693977&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33644693977

VL - 78

SP - 71

EP - 82

JO - Ars Combinatoria

JF - Ars Combinatoria

SN - 0381-7032

ER -