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More about Subcolorings

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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

A subcoloring is a vertex coloring of a graph in which every color class induces a disjoint union of cliques. We derive a number of results on the combinatorics, the algorithmics, and the complexity of subcolorings.

On the negative side, we prove that 2-subcoloring is NP-hard for comparability graphs, and that 3-subcoloring is NP-hard for AT-free graphs and for complements of planar graphs. On the positive side, we derive polynomial time algorithms for 2-subcoloring of complements of planar graphs, and for r-subcoloring of interval and of permutation graphs. Moreover, we prove asymptotically best possible upper bounds on the subchromatic number of interval graphs, chordal graphs, and permutation graphs in terms of the number of vertices.

The work of HJB and FVF is sponsored by NWO-grant 047.008.006. Part of the work was done while FVF was visiting the University of Twente, and while he was a visiting postdoc at DIMATIA-ITI (supported by GAČR 201/99/0242 and by the Ministry of Education of the Czech Republic as project LN00A056). FVF acknowledges support by EC contract IST-1999-14186: Project ALCOM-FT (Algorithms and Complexity - Future Technologies). JN acknowledges support of ITI - the Project LN00A056 of the Czech Ministery of Education. GJW acknowledges support by the START program Y43-MAT of the Austrian Ministry of Science.

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Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Twente, 7500, AE, Enschede, The Netherlands

    Hajo Broersma & Gerhard J. Woeginger

  2. Heinz Nixdorf Institute and Paderborn University, Fürstenallee 11, D-33102, Paderborn, Germany

    Fedor V. Fomin

  3. Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, 118 00, Prague, Czech Republic

    Jaroslav Nešetřil

Authors
  1. Hajo Broersma
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  2. Fedor V. Fomin
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  3. Jaroslav Nešetřil
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  4. Gerhard J. Woeginger
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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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Broersma, H., Fomin, F.V., Nešetřil, J., Woeginger, G.J. (2002). More about Subcolorings. 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_7

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  • DOI: https://doi.org/10.1007/3-540-36379-3_7

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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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