Acyclic edge coloring of planar graphs without 4-cycles

Weifan Wang (), Qiaojun Shu and Yiqiao Wang
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Weifan Wang: Zhejiang Normal University
Qiaojun Shu: Zhejiang Normal University
Yiqiao Wang: Academy of Mathematics and Systems Science

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 7, 562-586

Abstract: 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.

Keywords: Acyclic edge coloring; Planar graph; Cycle; Maximum degree (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-012-9474-y

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