Journal of Combinatorial Theory Series B
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Capturing Polynomial Time on Interval Graphs
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
| Hi-index | 48.22 |
We give a logical characterization of the polynomial-time properties of graphs with excluded minors: For every class C of graphs such that some graph H is not a minor of any graph in C, a property P of graphs in C is decidable in polynomial time if and only if it is definable in fixed-point logic with counting. Furthermore, we prove that for every class C of graphs with excluded minors there is a k such that a simple combinatorial algorithm, namely "the k-dimensional Weisfeiler--Lehman algorithm," decides isomorphism of graphs in C in polynomial time.