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 \(n_1, n_2, \ldots,n_n\) 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 \(n_1, n_2, \ldots, n_k\). In this paper, for 2-connected graphs, we generalize this result.