2-factors with the bounded number of components in line graphs

Let G be a simple graph of order n such that every vertex of degree 1 is adjacent to a vertex of degree at least 3. In this work, we prove that the line graph L(G) has a 2-factor with at most n-1/3 components if every odd branch-bond of G has a shortest branch of length 2. This is a best possible result which can be thought of as a counterpart of the main result in Fujisawa et al. (2007) [8].