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

For any positive integer ss, a [2,2s][2,2s]-factor in a graph GG is a connected even factor with maximum degree at most 2s2s. We prove that if every induced S(K1,2s+1)S(K1,2s+1) in a graph GG has at least three edges in a block of degree at most 2, then G2G2 has a [2,2s][2,2s]-factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].