The Reverse Mathematics and Uniform Relationships Between Theorems on Colouring of Planar Graphs
Year: 2026
Type: article
Abstract: Reverse mathematics is primarily interested in what set existence axioms are necessary and sufficient in a proof of a theorem. Much work has been done in classifying graph coloring theorems, studying k -regular graphs, k -chromatic graphs, and forests. This article takes inspiration from an old paper by Bean and studies graph coloring theorems restricted to planar graphs. Schmerl showed that these coloring theorems are all equivalent to WKL ${{\mathtt {WKL}}}$ monospace upper W upper K upper L over RCA 0 ${\mathtt {RCA}_{0}}$ monospace upper R upper C upper A 0 . In this article, we utilise Weihrauch reducibility to provide a deeper analysis on the uniformity of these implications. Whilst the proofs provided by Schmerl are not obviously non-uniform, we show that in many instances, non-uniformity is indeed necessary.
Source: Journal of Symbolic Logic
Authors: HEER TERN KOH, KENG MENG NG
Institution: Nanyang Technological University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7166146960
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