The Ck-extended graft construction

Gutjahr, Welzl and Woeginger found polynomial-time algorithms for a number of digraph homomorphism problems. These algorithms are based on the X-enumeration, the Ck-extended X-enumeration and the X-graft construction. In this note we show how the last two methods can be combined to obtain new polynomial-time algorithms, which also work for list homomorphisms. In the process we are able to extend results of Bang-Jensen and Hell, dealing with homomorphisms to bipartite tournaments, to list homomorphisms.