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Lower Bounds for On-line Graph Colorings

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Algorithms and Computation (ISAAC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8889))

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Abstract

We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use \(2\log _2 n - 10\) colors, where \(n\) is the number of vertices in the constructed graph. This is best possible up to an additive constant. The second strategy constructs graphs that contain neither \(C_3\) nor \(C_5\) as a subgraph and forces \(\varOmega (\frac{n}{\log n}^\frac{1}{3})\) colors. The best known on-line coloring algorithm for these graphs uses \(O(n^{\frac{1}{2}})\) colors.

This research is supported by: Polish National Science Center UMO-2011/03/D/ST6/01370.

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Authors and Affiliations

  1. Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland

    Grzegorz Gutowski, Jakub Kozik & Piotr Micek

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, China

    Xuding Zhu

  3. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

    Xuding Zhu

Authors
  1. Grzegorz Gutowski
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  2. Jakub Kozik
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  3. Piotr Micek
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  4. Xuding Zhu
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Corresponding author

Correspondence to Piotr Micek .

Editor information

Editors and Affiliations

  1. Pohang University of Science and Technology, Pohang, Korea, Republic of (South Korea)

    Hee-Kap Ahn

  2. Hankuk University of Foreign Studies, Yongin-si, Korea, Republic of (South Korea)

    Chan-Su Shin

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Gutowski, G., Kozik, J., Micek, P., Zhu, X. (2014). Lower Bounds for On-line Graph Colorings. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_40

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  • DOI: https://doi.org/10.1007/978-3-319-13075-0_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13074-3

  • Online ISBN: 978-3-319-13075-0

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