The existence of P_{\ge 3}-factor covered graphs
Jiancheng Wu, Tao Zhang, Sizhong Zhou · Discussiones Mathematicae Graph Theory · 2017
A spanning subgraph F of a graph G is called a P 3 -factor of G if every component of F is a path of order at least 3. A graph G is called a P 3factor covered graph if G has a P 3 -factor including e for any e E(G). In this paper, we obtain three sufficient conditions for graphs to be P 3 -factor covered graphs. Furthermore, it is shown that the results are sharp.