A comment to: On 3-colorable planar graphs without short cycles

TL;DR

This paper critiques a previous proof claiming certain planar graphs without specific short cycles are 3-colorable, highlighting issues in the original argument.

Contribution

It identifies errors in the existing proof of 3-colorability for planar graphs with restricted cycle structures.

Findings

The original proof contains inaccuracies.

Correctness of 3-colorability under these conditions is still unresolved.

Highlights the need for a valid proof or counterexamples.

Abstract

Let G be a graph. It was proved that if G is a planar graph without {4, 6, 7}-cycles and without two 5-cycles sharing exactly one edge, then G 3-colorable. We observed that the proof of this result is not correct.