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Acyclic Chromatic Index of 1-Planar Graphs

Author

Listed:
  • Wanshun Yang

    (School of Mathematics and Information Science, Weifang University, Weifang 261061, China)

  • Yiqiao Wang

    (School of Management, Beijing University of Chinese Medicine, Beijing 100029, China)

  • Weifan Wang

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Juan Liu

    (School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang 330038, China)

  • Stephen Finbow

    (Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada)

  • Ping Wang

    (Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada)

Abstract

The acyclic chromatic index χ a ′ ( G ) of a graph G is the smallest k for which G is a proper edge colorable using k colors. A 1-planar graph is a graph that can be drawn in plane such that every edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G has χ a ′ ( G ) ≤ Δ + 36 , where Δ denotes the maximum degree of G . This strengthens a result that if G is a triangle-free 1-planar graph, then χ a ′ ( G ) ≤ Δ + 16 .

Suggested Citation

  • Wanshun Yang & Yiqiao Wang & Weifan Wang & Juan Liu & Stephen Finbow & Ping Wang, 2022. "Acyclic Chromatic Index of 1-Planar Graphs," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2787-:d:881558
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