Toward a language theoretic proof of the four color theorem

Details Toward a language theoretic proof of the four color theorem Toward a language theoretic proof of the four color theorem

2010-06-07

arxiv.org/abs/1006.1324v2

Mathematics

Combinatorics

18 pages, many images; final version

Scientific paper

10.1016/j.aam.2011.11.002

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.

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