3 research outputs found
Cylindrical Graph Construction (definition and basic properties)
In this article we introduce the {\it cylindrical construction} for graphs
and investigate its basic properties. We state a main result claiming a weak
tensor-like duality for this construction. Details of our motivations and
applications of the construction will appear elsewhere
Combinatorial proof that subprojective constraint satisfaction problems are NP-complete
Abstract. We introduce a new general polynomial-time constructionthe fibre construction- which reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is any subprojective relational system. 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 system. The fibre construction allows us to prove the NP-completeness part of the conjectured Dichotomy Classification of CSPs, previously obtained by algebraic methods. We show that this conjectured Dichotomy Classification is equivalent to the dichotomy of whether or not the template is subprojective. This approach is flexible enough to yield NP-completeness of coloring problems with large girth and bounded degree restrictions thus reducing the Feder-Hell-Huang and Kostočka-Neˇsetˇril-Smolíková problems to the Dichotomy Classification of coloring problems. 1. Introduction and Previou