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

College of Mathematical Science, Tianjin Normal University, Tianjin City 300071, P.R. China

^* Corresponding author: dengyuqiu1980@126.com, xcdeng@mail.tjnu.edu.cn

Received: 1 December 2022
Accepted: 14 April 2023

Abstract

Let be a set which consists of some connected graphs. Let E be a spanning subgraph of graph G. It is called a -factor if every component of it is isomorphic to the element in . In this contribution, we give the lower bounds of four parameters (t(G), I(G), I′(G),bind (G)) of G, which force the graph G admits a ({K_1,i: q ≤ i ≤ 2q − 1} ∪ {K_2q+1})-factor for q ≥ 2 and a {P₂, P_2q+1}-factor for q ≥ 3 respectively. The tightness of the bounds are given.