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.
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Dinabandhu Pradhan
Vaishali Sharma
Riste Škrekovski
Discrete Mathematics
University of Ljubljana
Indian Institute of Technology Dhanbad
Higher Education Centre Novo Mesto
Building similarity graph...
Analyzing shared references across papers
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Pradhan et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69a75b7bc6e9836116a22de6 — DOI: https://doi.org/10.1016/j.disc.2026.115014