Abstract / Synopsis
The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.
A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.
Öhman, L. "A Beautiful Proof by Induction," Journal of Humanistic Mathematics, Volume 6 Issue 1 (January 2016), pages 73-85. DOI: 10.5642/jhummath.201601.06 . Available at: https://scholarship.claremont.edu/jhm/vol6/iss1/6