  The notion of friendliness between trees first appeared in solution of
Lando's problem on intersection of polyhedra in 3-space. A tree is friendly to
a path graph if edges of the tree can be numbered so that for each k,s the path
between the edges k and k+1 contains either both or none of the edges
k+2s,k+2s+1.
  Theorem. If a tree contains a path containing all vertices of degree greater
than 2, then the tree is friendly to a path graph.
  We also prove another sufficient condition for friendliness to a path graph
and a criterion for friendliness between trees, one of which has diameter 3.
