The Complexity of the List Homomorphism Problem for Graphs

We completely characterise the computational complexity of the list homomorphism problem for graphs in combinatorial and algebraic terms: for every graph H the problem is either NPcomplete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. The central result relies on an inductive definition of graphs whose problem is solvable in Logspace. A characterisation by forbidden subgraphs is given as well, and as a consequence, the metaproblem can be decided in polynomial time.

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: László Egri, Andrei A. Krokhin, Benoit Larose, Pascal Tesson
• Keywords: Computational Complexity, Descriptive Complexity Equivalents, List Homomorphism Problem, STACS 2010, Theoretical Computer Science