Digraph related constructions and the complexity of digraph homomorphism problems
Marcel Jackson, Tomasz Kowalski, Todd Niven · arXiv (Cornell University) · 2013
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we prove the algebraic CSP dichotomy conjecture holds for digraphs whose symmetric closure is a complete graph, and observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the subpowers algorithm if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of strict width and solvability by few subpowers are unstable under first order reductions.