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Acyclic edge coloring of planar graphs without 4-cycles

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Weifan Wang & Qiaojun Shu

  2. Academy of Mathematics and Systems Science, Beijing, 100080, China

    Yiqiao Wang

Authors
  1. Weifan Wang
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  2. Qiaojun Shu
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  3. Yiqiao Wang
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Corresponding author

Correspondence to Weifan Wang.

Additional information

Dedicated to Professor Gerard J. Chang on the occasion of his 60th birthday.

Research supported partially by NSFC (No. 11071223, No. 61170302), ZJNSF (No. Z6090150), ZSDZZZZXK08 and IP-OCNS-ZJNU.

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Wang, W., Shu, Q. & Wang, Y. Acyclic edge coloring of planar graphs without 4-cycles. J Comb Optim 25, 562–586 (2013). https://doi.org/10.1007/s10878-012-9474-y

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  • DOI: https://doi.org/10.1007/s10878-012-9474-y

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