Approximating Maximum Edge 2-Coloring in Simple Graphs

  • Zhi-Zhong Chen
  • Sayuri Konno
  • Yuki Matsushita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)


We present a polynomial-time approximation algorithm for legally coloring as many edges of a given simple graph as possible using two colors. It achieves an approximation ratio of roughly 0.842 and runs in O(n 3 m) time, where n (respectively, m) is the number of vertices (respectively, edges) in the input graph. The previously best ratio achieved by a polynomial-time approximation algorithm was \(\frac{5}{6}\approx 0.833\).


Approximation algorithms graph algorithms edge coloring NP-hardness 


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  1. 1.
    Chen, Z.-Z., Tanahashi, R.: Approximating Maximum Edge 2-Coloring in Simple Graphs via Local Improvement. Theoretical Computer Science (special issue on AAIM 2008) 410, 4543–4553 (2009)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Chen, Z.-Z., Tanahashi, R., Wang, L.: An Improved Approximation Algorithm for Maximum Edge 2-Coloring in Simple Graphs. Journal of Discrete Algorithms 6, 205–215 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Feige, U., Ofek, E., Wieder, U.: Approximating Maximum Edge Coloring in Multigraphs. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 108–121. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Gabow, H.: An Efficient Reduction Technique for Degree-Constrained Subgraph and Bidirected Network Flow Problems. In: Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC 1983), pp. 448–456. ACM, New York (1983)CrossRefGoogle Scholar
  5. 5.
    Hartvigsen, D.: Extensions of Matching Theory. Ph.D. Thesis, Carnegie-Mellon University (1984)Google Scholar
  6. 6.
    Hochbaum, D.: Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston (1997)Google Scholar
  7. 7.
    Jacobs, D.P., Jamison, R.E.: Complexity of Recognizing Equal Unions in Families of Sets. Journal of Algorithms 37, 495–504 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kawarabayashi, K., Matsuda, H., Oda, Y., Ota, K.: Path Factors in Cubic Graphs. Journal of Graph Theory 39, 188–193 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kosowski, A.: Approximating the Maximum 2- and 3-Edge-Colorable Subgraph Problems. Discrete Applied Mathematics 157, 3593–3600 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kosowski, A., Malafiejski, M., Zylinski, P.: Packing [1,Δ]-Factors in Graphs of Small Degree. Journal of Combinatorial Optimization 14, 63–86 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, Oxford (1987)zbMATHGoogle Scholar
  12. 12.
    Urrutia, J.: Art Gallery and Illumination Problems. In: Handbook on Computational Geometry. Elsevier Science, Amsterdam (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Zhi-Zhong Chen
    • 1
  • Sayuri Konno
    • 1
  • Yuki Matsushita
    • 1
  1. 1.Department of Mathematical SciencesTokyo Denki University, HatoyamaSaitamaJapan

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