Stability number and [ a,b ]‐factors in graphs

A spanning subgraph whose vertices have degrees belonging to the interval [ a,b ], where a and b are positive integers, such that a ≤ b , is called an [ a,b ]‐factor. In this paper, we prove sufficient conditions for existence of an [ a,b ]‐factor, a connected [ a,b ]‐factor, and a 2‐connected [ a,b ]‐factor. The conditions involve the minimum degree, the stability number, and the connectivity of a graph. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 254–264, 2004