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On the complexity of graph reconstruction

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Book cover Fundamentals of Computation Theory (FCT 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 529))

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Abstract

In the wake of the resolution of the four color conjecture, the graph reconstruction conjecture has emerged as one focal point of graph theory. This paper considers the computational complexity of decisions problems (deck checking and legitimate deck), the construction problems (preimage construction), and counting problems (preimage counting) related to the graph reconstruction conjecture. We show that:

  1. 1

    deck checking ℓ m graph isomorphism ℓ m legitimate deck, and

  2. 2

    if the graph reconstruction conjecture holds, then graph isomorphism ≡iso/l deck checking.

Relatedly, we display the first natural GI-hard NP set lacking obvious padding functions. Finally, we show that legitimate deck, preimage construction, and preimage counting are solvable in polynomial time on planar graphs, graphs with bounded genus, and partial k-trees for fixed k.

Research supported in part by the National Science Foundation under grants CCR-8809174/CCR-8996198 and CCR-8957604.

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Authors and Affiliations

  1. Fakultät Mathematik, Fredrich-Schiller-Universität, O-6900, Jena, Germany

    Dieter Kratsch

  2. Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA

    Lane A. Hemachandra

Authors
  1. Dieter Kratsch
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  2. Lane A. Hemachandra
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L. Budach

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© 1991 Springer-Verlag Berlin Heidelberg

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Kratsch, D., Hemachandra, L.A. (1991). On the complexity of graph reconstruction. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_76

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  • DOI: https://doi.org/10.1007/3-540-54458-5_76

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  • Print ISBN: 978-3-540-54458-6

  • Online ISBN: 978-3-540-38391-8

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