Toughness and binding number bounds of star-like and path factor

Abstract

Let $ \mathcal{L}$ be a set which consists of some connected graphs. LetEbe a spanning subgraph of graphG. It is called a $ \mathcal{L}$-factor if every component of it is isomorphic to the element in $ \mathcal{L}$. In this contribution, we give the lower bounds of four parameters (t(G), I(G), I′(G),bind (G)) ofG, which force the graphGadmits a ({K1,i:q ≤ i ≤ 2q − 1} ∪ {K2q+1})-factor forq ≥ 2 and a {P2, P2q+1}-factor forq ≥ 3 respectively. The tightness of the bounds are given.