Pk-factors in squares and line graphs of trees

Abstract

A Pk-factor H of G is a spanning subgraph of G such that each component of H is a path of k vertices, where k≥2. In this paper, we obtain two necessary conditions for Pk-factors in the squares and line graphs of trees, respectively. It is shown that the results are best possible in some sense. Furthermore, we give a characterization for a class of trees whose line graphs contain P4-factors.