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International Symposium on Algorithms and Computation

ISAAC 2014: Algorithms and Computation pp 516–527Cite as

An On-line Competitive Algorithm for Coloring \(P_8\)-free Bipartite Graphs

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

Abstract

The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced subgraphs, in particular for \(P_7\)-free bipartite graphs. We propose a new on-line competitive coloring algorithm for \(P_8\)-free bipartite graphs. Our proof technique improves the result, and shortens the proof, for \(P_7\)-free bipartite graphs.

V. Wiechert is supported by the Deutsche Forschungsgemeinschaft within the research training group ‘Methods for Discrete Structures’ (GRK 1408). P. Micek is supported by Polish National Science Center UMO-2011/03/D/ST6/01370.

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Author information

Authors and Affiliations

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

    Piotr Micek

  2. Technische Universität Berlin, Berlin, Germany

    Veit Wiechert

Authors
  1. Piotr Micek
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  2. Veit Wiechert
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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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© 2014 Springer International Publishing Switzerland

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Micek, P., Wiechert, V. (2014). An On-line Competitive Algorithm for Coloring \(P_8\)-free Bipartite Graphs. 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_41

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  • DOI: https://doi.org/10.1007/978-3-319-13075-0_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13074-3

  • Online ISBN: 978-3-319-13075-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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