2009/12/18 by Egri, Laszlo, Krokhin, Andrei, Larose, Benoit +1
#Computational Complexity (cs.CC) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.0912.3802
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-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.