Online Coloring of Bipartite Graphs with and without Advice

  • Maria Paola Bianchi
  • Hans-Joachim Böckenhauer
  • Juraj Hromkovič
  • Lucia Keller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)


In the online version of the well-known graph coloring problem, the vertices appear one after the other together with the edges to the already known vertices and have to be irrevocably colored immediately after their appearance. We consider this problem on bipartite, i.e., two-colorable graphs. We prove that 1.13747·log2 n colors are necessary for any deterministic online algorithm to color any bipartite graph on n vertices, thus improving on the previously known lower bound of log2 n + 1 for sufficiently large n.

Recently, the advice complexity was introduced as a method for a fine-grained analysis of the hardness of online problems. We apply this method to the online coloring problem and prove (almost) tight linear upper and lower bounds on the advice complexity of coloring a bipartite graph online optimally or using 3 colors. Moreover, we prove that \(O(\sqrt{n})\) advice bits are sufficient for coloring any graph on n vertices with at most ⌈log2 n⌉ colors.


Bipartite Graph Competitive Ratio Online Algorithm Additional Vertex Common Color 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maria Paola Bianchi
    • 1
  • Hans-Joachim Böckenhauer
    • 2
  • Juraj Hromkovič
    • 2
  • Lucia Keller
    • 2
  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoItaly
  2. 2.Department of Computer ScienceETH ZurichSwitzerland

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