Work

(2, 4)-Colorability of Planar Graphs Excluding Cycles with 3, 4, and 6 Vertices

Year: 2025

Type: article

Abstract: A defectivek-coloring is a coloring on the vertices of a graph with colors 1,2,…,k where adjacent vertices may have the same color. A (d1,d2)-coloring of a graph G is a defective two-coloring such that each vertex colored by i has at most di adjacent vertices of the same color, where i=1,2. A graph G is (d1,d2)-colorable if it admits (d1,d2)-coloring. For planar graphs excluding cycles with three, four, and six vertices, Dross and Ochem, and additionally Sittitrai and Pimpasalee, have studied their defective 2-coloring. They showed that such graphs are (0,6)- and (3,3)-colorable, respectively. We show in this work that these graphs are also (2,4)-colorable.

Source: Mathematics

DOI: 10.3390/math13111762

Authors: Pongpat Sittitrai, Wannapol Pimpasalee, Kittikorn Nakprasit

Institutions: Walailak University, Kalasin University, Khon Kaen University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Khon Kaen University, National Research Council of Thailand, Walailak University