Abstract
An ℱ-factor is a spanning subgraph H such that each connected component of H is isomorphic to some graph in ℱ. We use Pk and K1,r to denote the path of order k and the star of order r + 1, respectively. In particular, H is called a {P2, P3}-factor of G if ℱ = {P2, P3}; H is called a P≥k-factor of G if ℱ = {Pk, Pk+1,…}, where k ≥ 2; H is called an Sn-factor of G if ℱ = {P2, P3, K1,3,…, K1,n}, where n ≥ 2. A graph G is called a ℱ≥k-factor covered graph if there is a ℱ≥k-factor of G including e for any e ∈ E(G). We call a graph G is K1,r-free if G does not contain an induced subgraph isomorphic to K1,r. In this paper, we give a minimum degree condition for the K1,r-free graph with an Sn-factor and the K1,r-free graph with a ℱ≥3-factor, respectively. Further, we obtain sufficient conditions for K1,r-free graphs to be ℱ≥2-factor, ℱ≥3-factor or {P2, P3}-factor covered graphs. In addition, examples show that our results are sharp.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Guangdong Province
Subject
Management Science and Operations Research,Computer Science Applications,Theoretical Computer Science