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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 2009: SOFSEM 2009: Theory and Practice of Computer Science pp 401–412Cite as

A Problem Kernelization for Graph Packing

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5404))

Abstract

For a fixed connected graph H, we consider the NP-complete H-packing problem, where, given an undirected graph G and an integer k ≥ 0, one has to decide whether there exist k vertex-disjoint copies of H in G. We give a problem kernel of O(k |V(H)| − 1) vertices, that is, we provide a polynomial-time algorithm that reduces a given instance of H-packing to an equivalent instance with at most O(k |V(H)| − 1) vertices. In particular, this result specialized to H being a triangle improves a problem kernel for Triangle Packing from O(k 3) vertices by Fellows et al. [WG 2004] to O(k 2) vertices.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Hannes Moser

Authors
  1. Hannes Moser
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Editor information

Editors and Affiliations

  1. Aarhus Graduate School of Science, University of Aarhus, Ny Munkegade Bldg 1521-110, DK-8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Antonín Kučera

  3. Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, DK-8200, Aarhus N., Denmark

    Peter Bro Miltersen

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi  & Frank Valencia  & 

  5. Faculty of Mathematics and Physics, Charles University, Malostranské námestí 25, 118 00, Prague 1, Malá Strana, Czech Republic

    Petr Tůma

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Moser, H. (2009). A Problem Kernelization for Graph Packing. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_37

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  • DOI: https://doi.org/10.1007/978-3-540-95891-8_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95890-1

  • Online ISBN: 978-3-540-95891-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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