  This paper considers the problem of showing that every pair of binary trees
with the same number of leaves parses a common word under a certain simple
grammar. We enumerate the common parse words for several infinite families of
tree pairs and discuss several ways to reduce the problem of finding a parse
word for a pair of trees to that for a smaller pair. The statement that every
pair of trees has a common parse word is equivalent to the statement that every
planar graph is four-colorable, so the results are a step toward a language
theoretic proof of the four color theorem.
