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Complexity of graph covering problems

  • Jan Kratochvíl
  • Andrzej Proskurowski
  • Jan Arne Telle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 903)

Abstract

Given a fixed graph H, the H-cover problem asks whether an input graph G allows a degree preserving mapping fV(G)V(H) such that for every vV(G), f(N G (v))=N H (f(v)). In this paper, we design efficient algorithms for certain graph covering problems according to two basic techniques. The first one is a reduction to the 2-SAT problem. The second technique exploits necessary and sufficient conditions for the existence of regular factors in graphs. For other infinite classes of graph covering problems we derive NP-completeness results by reductions from graph coloring problems. We illustrate this methodology by classifying all graph covering problems defined by simple graphs with at most 6 vertices.

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References

  1. 1.
    J. Abello, M.R. Fellows and J.C. Stillwell, On the complexity and combinatorics of covering finite complexes, Australasian Journal of Combinatorics 4 (1991), 103–112Google Scholar
  2. 2.
    D. Angluin, Local and global properties in networks of processors, in Proceedings of the 12th STOC (1980), 82–93Google Scholar
  3. 3.
    D. Angluin and A. Gardner, Finite common coverings of pairs of regular graphs, Journal of Combinatorial Theory B 30 (1981), 184–187Google Scholar
  4. 4.
    N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1974Google Scholar
  5. 5.
    B. Courcelle and Y. Métivier, Coverings and minors: Applications to local computations in graphs, European Journal of Combinatorics 15 (1994), 127–138Google Scholar
  6. 6.
    M.R. Garey and D.S. Johnson, Computers and Intractability, W.H. Freeman and Co., 1978Google Scholar
  7. 7.
    F. Harary, Graph Theory, Addison-Wesley, 1969Google Scholar
  8. 8.
    P. Hell and J. Nešetřil, On the complexity of H-colouring, Journal of Combinatorial Theory B 48 (1990), 92–110Google Scholar
  9. 9.
    I. Holyer, The NP-completeness of edge-coloring, SIAM J. Computing 4 (1981), 718–720Google Scholar
  10. 10.
    D. König, Über graphen und ihre Andwendung auf Determinantentheorie und Mengenlehre, Math. Ann. 77, 1916, 453–465Google Scholar
  11. 11.
    J. Kratochvíl, Perfect codes in general graphs, monograph, Academia Praha (1991)Google Scholar
  12. 12.
    F.T. Leighton, Finite common coverings of graphs, Journal of Combinatorial Theory B 33 (1982), 231–238Google Scholar
  13. 13.
    J. Petersen, Die Theorie der regulären Graphen, Acta Mathematica 15 (1891), 193–220Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Jan Kratochvíl
    • 1
  • Andrzej Proskurowski
    • 2
  • Jan Arne Telle
    • 2
  1. 1.Charles UniversityPragueCzech Republic
  2. 2.University of OregonEugene

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