A spanning subgraph H of a graph G is a
$$P_{3}$$
-factor of G if every component of H is a path of order three. The square of a graph G, denoted by
$$G^{2}$$
, is the graph with vertex set V(G) such that two vertices are adjacent in
$$G^{2}$$
if and only if their distance in G is at most 2. A graph G is subcubic if it has maximum degree at most three. In this paper, we give a sharp necessary condition for the existence of
$$P_{3}$$
-factors in the square of a tree, which improves a result of Li and Zhang (Graphs Combin 24:107–111, 20...
