The Complexity of the List Homomorphism Problem for Graphs
We completely classify the computational complexity of the list -colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph , the problem is either -complete, -complete, -complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.
complexity list homomorphism datalog constraint satisfaction problem universal algebra