Bounds of Two Toughnesses and Binding Numbers for Star Factors
Yujia Gao, Zhen Ji, Xiaojie Sun, Qinghe Tong · Journal of Interconnection Networks · 2024
For a set [Formula: see text] of connected graphs, a spanning subgraph [Formula: see text] of a graph [Formula: see text] is an [Formula: see text]-factor if every component of [Formula: see text] is isomorphic to some member of [Formula: see text]. In this paper, we give a criterion for the existence of tight toughness, isolated toughness and binding number bounds in a graph of a strong [Formula: see text]-star factor, [Formula: see text]-factor and [Formula: see text]-star factor. Moreover, we show that the bounds of the sufficient conditions are sharp.