Relating Partial and Complete Solutions and the Complexity of Computing Smallest Solutions

  • André Große
  • Jörg Rothe
  • Gerd Wechsung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2202)


We prove that computing a single pair of vertices that are mapped onto each other by an isomorphism ϕ between two isomorphic graphs is as hard as computing ϕ itself.Th is result optimally improves upon a result of Gál et al.W e establish a similar, albeit slightly weaker, result about computing complete Hamiltonian cycles of a graph from partial Hamiltonian cycles.W e also show that computing the lexicographically first four-coloring for planar graphs is δ 2 p -hard. This result optimally improves upon a result of Khuller and Vazirani who prove this problem to be NP-hard, and conclude that it is not self-reducible in the sense of Schnorr, assuming P ≠ NP. W e discuss this application to non-self-reducibility and provide a general related result.


partial solutions complexity of smallest solutions selfreducibility graph isomorphisms Hamiltonian cycles graph colorability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • André Große
    • 1
  • Jörg Rothe
    • 2
  • Gerd Wechsung
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Math. InstitutHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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