This has a fix for the definition for V_0 on page 63. Because we later contract nodes with Leaf_Y(u)=Leaf_Y(v) it does not matter if we "root" V_0 to be such that V_0={ Leaf_Y(v)=0 and |Leaf_Y(parent(v))|>=1}. However, it might be clearer and I don't see anything that speaks against it.
This has a fix for the definition for V_0 on page 63. Because we later contract nodes with Leaf_Y(u)=Leaf_Y(v) it does not matter if we "root" V_0 to be such that V_0={ Leaf_Y(v)=0 and |Leaf_Y(parent(v))|>=1}. However, it might be clearer and I don't see anything that speaks against it.