Tight Toughness, Isolated Toughness and Binding Number Bounds for the [1,n]-Factors and the {K2,Ci≥4}-Factors

Abstract

Let [Formula: see text] be an integer. The [Formula: see text]-factor of a graph [Formula: see text] is a spanning subgraph [Formula: see text] if [Formula: see text] for all [Formula: see text], and the [Formula: see text]-factor is a subgraph whose each component is either [Formula: see text] or [Formula: see text]. In this paper, we give the lower bounds with regard to tight toughness, isolated toughness and binding number to guarantee the existence of the [Formula: see text]-factors and [Formula: see text]-factors for a graph.