Given a graph H , let b(H) be the minimum integer b, if it exists, for which H -colouring is N P-complete when restricted to instances with degree bounded by b. We show that b(H) exists for any non-bipartite graph. This verifies for graphs the conjecture of Feder, Hell, and Huang that any CSP that is N P-complete, is N P-complete for instances of some maximum degree. Furthermore, we show the same for all projective CSPs, and we get constant upper bounds on the parameter b for various infinite… CONTINUE READING