Connected even factors in the square of essentially 2-edge connected   graphs
  In this paper we prove that the square of an essentially 2-edge connected graph with an additional property has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge connected graph does not contain a connected even factor with bounded maximum degree. 
Jan Ekstein, Baoyindureng Wu, and Liming Xiong
math.CO