Combinatorial Proof that Subprojective Constraint Satisfaction Problems are NP-Complete

  • Jaroslav Nešetřil
  • Mark Siggers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


We introduce a new general polynomial-time construction- the fibre construction- which reduces any constraint satisfaction problem \({\rm CSP}(\mathcal H)\) to the constraint satisfaction problem \({\rm CSP}(\mathcal{P})\), where \({\mathcal{P}}\) is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that \({\rm CSP}(\mathcal{P})\) is NP-complete for any subprojective (and thus also projective) relational structure. This provides a starting point for a new combinatorial approach to the NP-completeness part of the conjectured Dichotomy Classification of CSPs, which was previously obtained by algebraic methods. This approach is flexible enough to yield NP-completeness of coloring problems with large girth and bounded degree restrictions.


Relational Structure Constraint Satisfaction Constraint Satisfaction Problem Homomorphic Image Universal Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Mark Siggers
    • 1
  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University Malostranské nám. 25, 11800 Praha 1Czech Republic

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