A Degree Sum Condition for the Existence of a Path-Factor

Abstract

Let $G$ be a connected graph of order $n$, and suppose that $n=\sum _{i=1}^k{n}_i$, where $n_1,n_2,\dots ,n_n$ are integers with at least two. A spanning subgraph is called a path-factor if each component of it is a path of order at least two. In [Y. Chen, F. Tian, B, Wei, Degree sums and path-factors in graphs, Graphs and Combin. $17(2001),61-71.]$, Chen et al. gave a degree sum condition for the existence of a path-factor consisting of paths of order $n_1,n_2,\dots ,n_k$. In this paper, for 2-connected graphs, we generalize this result.