Spectral radius and [a,b]-factors in graphs

Abstract

An [a,b]-factor of a graph G is a spanning subgraph H such that a≤dH(v)≤b for each v∈V(G). In this paper, we provide spectral conditions for the existence of an odd [1,b]-factor in a connected graph with minimum degree δ and the existence of an [a,b]-factor in a graph, respectively. Our results generalize and improve some previous results on perfect matchings of graphs. For a=1, we extend the result of O [31] to obtain an odd [1,b]-factor and further generalize the result of Liu, Liu and Feng [28] for a=b=1. For n≥3a+b−1, we confirm the conjecture of Cho, Hyun, O and Park [5]. We conclude some open problems in the end.