  For any positive integer $s$, a $[2,2s]$-factor in a graph $G$ is a connected
even factor with maximum degree at most $2s$. We prove that if every induced
$S(K_{1, 2s+1})$ in a graph $G$ has at least 3 edges in a block of degree at
most two, then $G^2$ has a $[2,2s]$-factor. This extends the results of Hendry
and Vogler and of Abderrezzak et al.
