Colouring Pairs of Binary Trees: Results and Problems
  Alan Gibbons and Paul Sant

Abstract:

In this talk I shall discuss some results concerning
the so-called "Colouring Pairs of Binary Trees" problem
(CPBT). CPBT involves finding a proper 3-edge colouring 
of a pair of binary trees, T_i and T_j, such that the colours 
of edgesadjacent to the leaves of T_i and T_j are the same.

I will discuss two approaches to solving CPBT and mention some
of the remaining problems to solving CPBT