Skip to main content
SpringerLink
Log in

Acyclic chromatic indices of planar graphs with girth at least five

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

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. In this paper, we prove that every planar graph G with girth g(G)≥5 and maximum degree Δ≥12 has a′(G)=Δ.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alon N, Zaks A (2002) Algorithmic aspects of acyclic edge coloring colorings. Algorithmica 32:611–614

    Article  MATH  MathSciNet  Google Scholar 

  • Alon N, McDiarmid C, Reed B (1991) Acyclic coloring of graphs. Random Struct Algorithms 2:277–288

    Article  MATH  MathSciNet  Google Scholar 

  • Alon N, Sudakov B, Zaks A (2001) Acyclic edge-colorings of graphs. J Graph Theory 37:157–167

    Article  MATH  MathSciNet  Google Scholar 

  • Basavaraju M, Chandran LS (2009) Acyclic edge coloring of planar graphs. http://arxiv.org/abs/0908.2237v1

  • Borowiecki M, Fiedorowicz A (2010) Acyclic edge coloring of planar graphs without short cycles. Discrete Math 310:1445–1455

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen N, Havet F (2009) Acyclic edge-colouring of planar graphs. Extended abstract. Electron Not Discrete Math 34:417–421. (Euro-Comb 2009)

    Article  Google Scholar 

  • Cohen N, Havet F, Müller T (2009) Acyclic edge-colouring of planar graphs. INRIA Research Report, RR-6876

  • Fiedorowicz A, Haluszczak M, Narayanan N (2008) About acyclic edge colourings of planar graphs. Inf Process Lett 108:412–417

    Article  MathSciNet  Google Scholar 

  • Hou J, Wu J, Liu G, Liu B (2008) Acyclic edge colorings of planar graphs and series-parallel graphs. Sci China Ser A 38:1335–1346

    Google Scholar 

  • Hou J, Wu J, Liu G, Liu B (2010) Acyclic edge chromatic number of outerplanar graphs. J Graph Theory 64:22–36

    MATH  MathSciNet  Google Scholar 

  • Molloy M, Reed B (1998) Further algorithmic aspects of Lovász local lemma. In: Proceedings of the 30th annual ACM symposium on theory of computing, pp 524–529

  • Muthu R, Narayanan N, Subramanian CR (2006) Improved bounds on acyclic edge coloring. Electron Not Discrete Math 19:171–177

    Article  MathSciNet  Google Scholar 

  • Něsetřil J, Wormald N (2005) The acyclic edge chromatic number of a random d-regular graph is d+1. J Graph Theory 49:69–74

    Article  MATH  MathSciNet  Google Scholar 

  • Skulrattanakulchai S (2004) Acyclic colorings of subcubic graphs. Inf Process Lett 92:161–167

    Article  MATH  MathSciNet  Google Scholar 

  • Vizing V (1964) On an estimate of the chromatic index of a p-graph. Diskretn Anal 3:25–30

    MathSciNet  Google Scholar 

  • Wang W, Shu Q, Wang P (2009) Acyclic chromatic indices of planar graphs with large girth, submitted

  • Yu D, Hou J, Liu G, Liu B, Xu L (2009) Acyclic edge coloring of planar graphs with large girth. Theor Comput Sci 410:5196–5200

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Qiaojun Shu & Weifan Wang

Authors
  1. Qiaojun Shu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weifan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weifan Wang.

Additional information

Research supported partially by NSFC (Nos. 10771197, 11071223) and ZJNSF (No. Z6090150).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shu, Q., Wang, W. Acyclic chromatic indices of planar graphs with girth at least five. J Comb Optim 23, 140–157 (2012). https://doi.org/10.1007/s10878-010-9354-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-010-9354-2

Keywords

Search

Navigation