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The Packing Coloring Problem for (q,q-4) Graphs

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Combinatorial Optimization (ISCO 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7422))

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Abstract

It is known that computing the packing chromatic number of a graph is an NP-hard problem, even when restricted to tree graphs. This fact naturally leads to the search of graph families where this problem is polynomial time solvable.

Babel et al. (2001) showed that a large variety of NP-complete problems can be efficiently solved for the class of (q,q − 4) graphs, for every fixed q.

In this work we show that also to compute the packing chromatic number can be efficiently solved for the class of (q,q − 4) graphs.

Partially supported by grants CONICET PIP 0241 (2010-2012) and PID UNR 254 (2009-2012).

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References

  1. Argiroffo, G., Nasini, G., Torres, P.: Polynomial instances of the Packing Coloring Problem. To appear in Discrete Applied Mathematics

    Google Scholar 

  2. Babel, L.: On the P 4 structure of graphs. Habilitationsschrift, Technische Universitat Munchen (1997)

    Google Scholar 

  3. Babel, L., Kloks, T., Kratochvíl, J., Kratsch, D., Müller, H., Olariu, S.: Efficient algorithms for graphs with few P 4’s. Discrete Mathematics 235, 29–51 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Babel, L., Olariu, S.: On the structure of graphs with few P 4’s. Discrete Applied Mathematics 84, 1–13 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Brešar, B., Klavžar, S., Rall, D.F.: On the packing chromatic numbers of cartesian products, hexagonal lattice, and trees. Discrete Applied Mathematics 155, 2303–2311 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Courcelle, B., Makouski, J.A., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique width. Theory of Computing Sistems 33, 125–150 (2000)

    Article  MATH  Google Scholar 

  7. Courcelle, B., Olariu, S.: Upper bounds to the clique-width of graphs. Discrete Applied Mathematics 101, 77–114 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fiala, J., Golovach, P.A.: Complexity of the packing coloring problem of trees. Discrete Applied Mathematics 158, 771–778 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Giakoumakis, V., Roussel, H., Thuillier, H.: On P4-tidy graphs. Discrete Mathematics and Theoretical Computer Science 1, 17–41 (1997)

    MathSciNet  MATH  Google Scholar 

  10. Goddard, W., Hedetniemi, S.M., Hedetniemi, S.T., Harris, J.M., Rall, D.F.: Broadcast Chromatic Numbers of Graphs. Ars Combinatoria 86, 33–49 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Graph Classes, http://www.graphclasses.org/classes/gc_498.html

  12. Jamison, B., Olariu, S.: P-components and the homogeneous decomposition of graphs. SIAM J. Discrete Math. 8, 448–463 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jamison, B., Olariu, S.: Recognizing P4-sparse graphs in linear time. SIAM Journal on Comput. 21, 381–406 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jamison, B., Olariu, S.: A tree representation for P4-sparse graphs. Discrete Applied Mathematics 35, 115–129 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Argentina

    G. Argiroffo, G. Nasini & P. Torres

  2. CONICET, Argentina

    G. Nasini & P. Torres

Authors
  1. G. Argiroffo
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  2. G. Nasini
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  3. P. Torres
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Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    A. Ridha Mahjoub  & Vangelis Th. Paschos  & 

  2. Department of Informatics, Athens University of Economics and Business, 76 Patission str., 10434, Athens, Greece

    Vangelis Markakis  & Ioannis Milis  & 

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© 2012 Springer-Verlag Berlin Heidelberg

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Argiroffo, G., Nasini, G., Torres, P. (2012). The Packing Coloring Problem for (q,q-4) Graphs. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_28

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  • DOI: https://doi.org/10.1007/978-3-642-32147-4_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32146-7

  • Online ISBN: 978-3-642-32147-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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