Star subdivisions and connected even factors in the square of a graph
  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. 
Jan Ekstein, P\v{r}emysl Holub, Tom\'a\v{s} Kaiser, Liming Xiong,   Shenggui Zhang
math.CO