A remark on a result on odd colorings of planar graphs
Abstract
A proper k -coloring of a graph is said to be odd if every non-isolated vertex has a color that appears an odd number of times on its neighborhood. Miao et al. (2024) [2] claimed that every planar graph without adjacent 3-cycles is odd 7-colorable and every triangle-free planar graph without intersecting 4-cycles is odd 5-colorable. Here, we point out that their published proof contains a fundamental flaw which affects the validity of the main results.
Fields of Study & Subjects
Advanced Graph Theory Research
Limits and Structures in Graph Theory
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Discrete Mathematics
- Publisher
- Elsevier BV
- Volume
- 349
- Issue
- 6
- Pages
- 115014–115014
- Publication date
- 27 January 2026
- Language
- EN