Toward a language theoretic proof of the four color theorem
Combinatorics
2014-04-18 v2
Abstract
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.
Cite
@article{arxiv.1006.1324,
title = {Toward a language theoretic proof of the four color theorem},
author = {Bobbe Cooper and Eric Rowland and Doron Zeilberger},
journal= {arXiv preprint arXiv:1006.1324},
year = {2014}
}
Comments
18 pages, many images; final version