Degree conditions for path-factors in graphs

A spanning subgraph H of a graph G is called a path-factor if every component of H is a path. Wang and Zhang Degree conditions for the existence of a \P₂, P₅\-factor in a graph, RAIRO: Oper. Res. 57 (2023), 2231-2237 conjectured that a connected graph G with (G) 5 contains a \P₂, P₅\-factor if (G) 3 (G) -14, where (G) and (G) denote the minimum degree and independence number of G, respectively. We show that the conjecture is true except G X 7K₃, where X is a spanning subgraph of K₃. Furthermore, we give two degree conditions for the existence of \P₂, P₅\-factors, one of which is a stronger version of Wang's another conjecture. We also show the degree conditions are best possible.