### 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 |
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Pages (from-to) | 71-82 |

Number of pages | 12 |

Journal | Ars Combinatoria |

Volume | 78 |

Publication status | Published - 2006 Jan 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)