Combinatorial proof that subprojective constraint satisfaction problems are NP-complete

Abstract

We introduce a new general polynomial-time construction-the fibre construction- which reduces any constraint satisfaction problem CSP(ℋ) to the constraint satisfaction problem CSP(P), where P is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that CSP(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. © Springer-Verlag Berlin Heidelberg 2007.