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Acyclic edge coloring of planar graphs without 4-cycles

Author

Listed:
  • Weifan Wang

    (Zhejiang Normal University)

  • Qiaojun Shu

    (Zhejiang Normal University)

  • Yiqiao Wang

    (Academy of Mathematics and Systems Science)

Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a′(G) of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiamčik (Math. Slovaca 28:139–145, 1978) and later Alon, Sudakov and Zaks (J. Graph Theory 37:157–167, 2001) conjectured that a′(G)≤Δ+2 for any simple graph G with maximum degree Δ. In this paper, we confirm this conjecture for planar graphs G with Δ≠4 and without 4-cycles.

Suggested Citation

  • Weifan Wang & Qiaojun Shu & Yiqiao Wang, 2013. "Acyclic edge coloring of planar graphs without 4-cycles," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 562-586, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-012-9474-y
    DOI: 10.1007/s10878-012-9474-y
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    References listed on IDEAS

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    1. Qiaojun Shu & Weifan Wang, 2012. "Acyclic chromatic indices of planar graphs with girth at least five," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 140-157, January.
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