Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Regular Article: On search, decision, and the efficiency of polynomial-time algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
SIAM Journal on Discrete Mathematics
On computing graph minor obstruction sets
Theoretical Computer Science
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph minors. XXI. Graphs with unique linkages
Journal of Combinatorial Theory Series B
Graph minors XXIII. Nash-Williams' immersion conjecture
Journal of Combinatorial Theory Series B
A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
Finding topological subgraphs is fixed-parameter tractable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
Hi-index | 0.00 |
In the final paper of the Graph Minors series [Neil Robertson and Paul D. Seymour. Graph minors XXIII. Nash-Williams' immersion conjectureJ. Comb. Theory, Ser. B, 100(2):181---205, 2010.], N. Robertson and P. Seymour proved that graphs are well-quasi-ordered with respect to the immersion relation. A direct implication of this theorem is that each class of graphs that is closed under taking immersions can be fully characterized by forbidding a finite set of graphs (immersion obstruction set). However, as the proof of the well-quasi-ordering theorem is non-constructive, there is no generic procedure for computing such a set. Moreover, it remains an open issue to identify for which immersion-closed graph classes the computation of those sets can become effective. By adapting the tools that where introduced in [Isolde Adler, Martin Grohe and Stephan Kreutzer. Computing excluded minors, SODA, 2008: 641-650.] for the effective computation of obstruction sets for the minor relation, we expand the horizon of the computability of obstruction sets for immersion-closed graph classes. In particular, we prove that there exists an algorithm that, given the immersion obstruction sets of two graph classes that are closed under taking immersions, outputs the immersion obstruction set of their union.