The Complexity of the List Homomorphism Problem for Graphs

László Egri, Andrei Krokhin, Benoit Larose & Pascal Tesson
We completely classify the computational complexity of the list $\bH$-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph $\bH$ 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.
This data repository is not currently reporting usage information. For information on how your repository can submit usage information, please see our documentation.