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

Author

Listed:
  • Pongpat Sittitrai

    (Futuristic Science Research Center, School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand
    Research Center for Theoretical Simulation and Applied Research in Bioscience and Sensing, Walailak University, Nakhon Si Thammarat 80160, Thailand)

  • Wannapol Pimpasalee

    (Department of Science and Mathematics, Faculty of Science and Health Technology, Kalasin University, Kalasin 46000, Thailand)

  • Kittikorn Nakprasit

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

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 ( d 1 , d 2 ) - coloring of a graph G is a defective two-coloring such that each vertex colored by i has at most d i adjacent vertices of the same color, where i = 1 , 2 . A graph G is ( d 1 , d 2 ) - colorable if it admits ( d 1 , d 2 ) -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.

Suggested Citation

  • Pongpat Sittitrai & Wannapol Pimpasalee & Kittikorn Nakprasit, 2025. "(2, 4)-Colorability of Planar Graphs Excluding Cycles with 3, 4, and 6 Vertices," Mathematics, MDPI, vol. 13(11), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1762-:d:1664632
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