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

Jianxiang Li, Haruhide Matsuda

Research output: Contribution to journalArticle

6 Citations (Scopus)

### 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 71-82 12 Ars Combinatoria 78 Published - 2006 Jan 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.

In: Ars Combinatoria, Vol. 78, 01.2006, p. 71-82.

Research output: Contribution to journalArticle

Li, Jianxiang ; Matsuda, Haruhide. / On (g, f, n)-critical graphs. In: Ars Combinatoria. 2006 ; Vol. 78. pp. 71-82.
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