On Simultaneous 2-locally-balanced 2-partition for Two Forests with Same   Vertices
  The existence of a partition of the common set of the vertices of two forests into two subsets, when difference of their capacities in the neighborhood of each vertex of each forest not greater than 2 is proved, and an example, which shows that improvement of the specified constant is impossible is brought. 
Hovhannes G. Tananyan, Rafayel R. Kamalian
math.CO cs.DM