Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).
- [a, b]-factor
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics