A remark on a result on odd colorings of planar graphs

IF 1.1 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2026-06-01 Epub Date: 2026-01-27 DOI:10.1016/j.disc.2026.115014

Dinabandhu Pradhan , Vaishali Sharma , Riste Škrekovski

引用次数: 0

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.

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关于平面图奇色的一个结果的注解

如果每个非孤立顶点的颜色在其邻域上出现奇数次，则称图的适当k-着色为奇数。Miao et al.(2024)[2]提出无相邻3环的平面图都是奇7色，无4环相交的无三角形平面图都是奇5色。在此，我们指出他们发表的证明存在一个影响主要结果有效性的根本性缺陷。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.