Star subdivisions and connected even factors in the square of a graph

For any positive integer s , a [ 2 , 2 s ] -factor in a graph G is a connected even factor with maximum degree at most 2 s . We prove that if every induced S ( K 1 , 2 s + 1 ) in a graph G has at least three edges in a block of degree at most 2, then G 2 has a [ 2 , 2 s ] -factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].