# A neighborhood condition for graphs to have [a, b]-factors II

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4 Citations (Scopus)

### Abstract

Let a, b, m, and t be integers such that 1 ≤ a < b and 1 ≤ t ≤ [(b - m + 1)/a]. Suppose that G is a graph of order |G| and H is any subgraph of G with the size |E(H)| = m. Then we prove that G has an [a, b]-factor containing all the edges of H if the minimum degree is at least a, |G| > ((a + b)(t(a + b - 1) - 1) + 2m)/b, and |NG(x1) ∪... ∪NG(xt)| ≥ (a|G| + 2m)/(a + b) for every independent set {x1,..., xt} ⊆ V (G). This result is best possible in some sense and it is an extension of the result of H. Matsuda (A neighborhood condition for graphs to have [a, b]-factors, Discrete Mathematics 224 (2000) 289-292).

Original language English 763-768 6 Graphs and Combinatorics 18 4 https://doi.org/10.1007/s003730200062 Published - 2002 Yes

### ASJC Scopus subject areas

• Mathematics(all)
• Discrete Mathematics and Combinatorics

### Cite this

In: Graphs and Combinatorics, Vol. 18, No. 4, 2002, p. 763-768.

Research output: Contribution to journalArticle

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abstract = "Let a, b, m, and t be integers such that 1 ≤ a < b and 1 ≤ t ≤ [(b - m + 1)/a]. Suppose that G is a graph of order |G| and H is any subgraph of G with the size |E(H)| = m. Then we prove that G has an [a, b]-factor containing all the edges of H if the minimum degree is at least a, |G| > ((a + b)(t(a + b - 1) - 1) + 2m)/b, and |NG(x1) ∪... ∪NG(xt)| ≥ (a|G| + 2m)/(a + b) for every independent set {x1,..., xt} ⊆ V (G). This result is best possible in some sense and it is an extension of the result of H. Matsuda (A neighborhood condition for graphs to have [a, b]-factors, Discrete Mathematics 224 (2000) 289-292).",
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