Data structures and network algorithms
Data structures and network algorithms
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Graph minors. IX. Disjoint crossed paths
Journal of Combinatorial Theory Series B
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Graph minors. XI.: circuits on a surface
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Graph minors XIV: extending an embedding
Journal of Combinatorial Theory Series B
Graph minors. XII: distance on a surface
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Dimension Reduction in the \ell _1 Norm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Excluding any graph as a minor allows a low tree-width 2-coloring
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
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
A Separator Theorem in Minor-Closed Classes
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Contraction decomposition in h-minor-free graphs and algorithmic applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Linear kernels for (connected) dominating set on H-minor-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
List-coloring graphs without subdivisions and without immersions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Structure theorem and isomorphism test for graphs with excluded topological subgraphs
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
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At the core of the Robertson-Seymour theory of graph minors lies a powerful decomposition theorem which captures, for any fixed graph H, the common structural features of all the graphs which do not contain H as a minor. Robertson and Seymour used this result to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation, as well as give a polynomial time algorithm for the disjoint paths problem when the number of the terminals is fixed. The theorem has since found numerous applications, both in graph theory and theoretical computer science. The original proof runs more than 400 pages and the techniques used are highly non-trivial. In this paper, we give a simplified algorithm for finding the decomposition based on a new constructive proof of the decomposition theorem for graphs excluding a fixed minor H. The new proof is both dramatically simpler and shorter, making these results and techniques more accessible. The algorithm runs in time O(n3), as does the original algorithm of Robertson and Seymour. Moreover, our proof gives an explicit bound on the constants in the O notation, whereas the original proof of Robertson and Seymour does not.