A combinatorial constraint satisfaction problem dichotomy classification conjecture

As with our previous version of the fibre construction, we are able to address restricted versions of the dichotomy conjecture. In particular, we reduce the Feder-Hell-Huang conjecture to the CSP dichotomy classification conjecture, and we prove the Kostochka-NeÅ¡etřil-Smolíková conjecture. Although these results were proved independently by Jonsson et al. and Kun respectively, we give different, shorter, proofs.