Reducibility in the Four-Color Theorem

TL;DR

This paper provides additional details and original computer programs for a simplified, computer-assisted proof of the Four-Color Theorem, enhancing transparency and reproducibility of the original verification.

Contribution

It offers detailed explanations and the original computational tools for a key lemma in a simplified proof of the Four-Color Theorem.

Findings

Verification of the key lemma using computer programs

Enhanced transparency of the proof process

Supporting data and code for reproducibility

Abstract

In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have verified those statements using a computer. Here we give additional details for one of those lemmas, and we include the original computer programs and data as "ancillary files" accompanying this submission.