Tight Toughness, Isolated Toughness and Binding Number Bounds for Some Factors and Some Factor-Deleted Graphs

For a set [Formula: see text] of connected graphs, a spanning subgraph [Formula: see text] of a graph [Formula: see text] is called an [Formula: see text]-factor if each component of [Formula: see text] is isomorphic to a member of [Formula: see text]. In this paper, we obtain a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of a [Formula: see text]-factor, two sufficient conditions to guarantee the existence of a [Formula: see text]-factor in a bipartite graph and some sufficient conditions for [Formula: see text]-factor deleted graph and a [Formula: see text]-factor deleted graph.