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Acyclic Edge Coloring of 4-Regular Graphs Without 3-Cycles

  • Qiaojun Shu
  • Yiqiao Wang
  • Yulai Ma
  • Weifan Wang
Article

Abstract

A proper edge coloring is called acyclic if no bichromatic cycles are produced. It was conjectured that every simple graph G with maximum degree \(\varDelta \) is acyclically edge-\((\varDelta +2)\)-colorable. Basavaraju and Chandran (J Graph Theory 61:192–209, 2009) confirmed the conjecture for non-regular graphs G with \(\varDelta =4\). In this paper, we extend this result by showing that every 4-regular graph G without 3-cycles is acyclically edge-6-colorable.

Keywords

Acyclic edge coloring 4-Regular graph Cycle 

Mathematics Subject Classification

05C15 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Qiaojun Shu
    • 1
  • Yiqiao Wang
    • 2
  • Yulai Ma
    • 3
  • Weifan Wang
    • 3
  1. 1.School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.School of ManagementBeijing University of Chinese MedicineBeijingChina
  3. 3.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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