Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Graph minors. XVIII. tree-decompositions and well-quasi-ordering
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Applying the Graph Minor Theorem to the Verification of Graph Transformation Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
A well-quasi-order for tournaments
Journal of Combinatorial Theory Series B
Finding topological subgraphs is fixed-parameter tractable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Well-quasi-ordering hereditarily finite sets
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Algorithms for finding a maximum non-k-linked graph
ESA'11 Proceedings of the 19th European conference on Algorithms
List-coloring graphs without subdivisions and without immersions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
FPT suspects and tough customers: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Effective computation of immersion obstructions for unions of graph classes
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Well-structured graph transformation systems with negative application conditions
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
Characterizing graphs of small carving-width
Discrete Applied Mathematics
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
| Hi-index | 0.00 |
We define a quasi-order of the class of all finite hypergraphs, and prove it is a well-quasi-order. This has two corollaries of interest:*Wagner's conjecture, proved in a previous paper, states that for every infinite set of finite graphs, one of its members is a minor of another. The present result implies the same conclusion even if the vertices or edges of the graphs are labelled from a well-quasi-order and we require the minor relation to respect the labels. *Nash-Williams' ''immersion'' conjecture states that in any infinite set of finite graphs, one can be ''immersed'' in another; roughly, embedded such that the edges of the first graph are represented by edge-disjoint paths of the second. The present result implies this, in a strengthened form where we permit vertices to be labelled from a well-quasi-order and require the immersion to respect the labels.