Work

A remark on a result on odd colorings of planar graphs

Year: 2026

Type: article

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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115014

Authors: Dinabandhu Pradhan, Vaishali Sharma, Riste Škrekovski

Institutions: Indian Institute of Technology Dhanbad, University of Ljubljana, Rudolfovo – Science and Technology Centre Novo mesto

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funder: Javna Agencija za Raziskovalno Dejavnost RS