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On the b-Chromatic Number of Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

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Abstract

The b-chromatic number b(G) of a graph G = (V,E) is the largest integer k such that G admits a vertex partition into k independent sets X i (i = 1, . . . , k) such that each X i contains a vertex x i adjacent to at least one vertex of each X j , j ≠ i. We discuss on the tightness of some bounds on b(G) and on the complexity of determining b(G). We also determine the asymptotic behavior of b(G n,p ) for the random graph, within the accuracy of a multiplicative factor 2 + o(1) as n→∞.

Supported by the Ministery of Education of the Czech Republic as project LN00A056.

Research supported in part by the Hungarian Research Fund under grant OTKA T-032969.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jan Kratochvíl

  2. Computer and Automation Institute, Hungarian Academy of Sciences, Kende ú 13-17, H-1111, Budapest

    Zsolt Tuza

  3. Insitut für Mathematik, Technische Universität Ilmenau, D-98684, Ilmenau, Germany

    Margit Voigt

Authors
  1. Jan Kratochvíl
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  2. Zsolt Tuza
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  3. Margit Voigt
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

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© 2002 Springer-Verlag Berlin Heidelberg

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Kratochvíl, J., Tuza, Z., Voigt, M. (2002). On the b-Chromatic Number of Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_27

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  • DOI: https://doi.org/10.1007/3-540-36379-3_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

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