Graph minors. VI. Disjoint paths across a disc
Journal of Combinatorial Theory Series B
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Graph minors. IX. Disjoint crossed paths
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
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)
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Coloring triangle-free graphs on surfaces
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Algorithms for finding an induced cycle in planar graphs and bounded genus graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph minors. XXI. Graphs with unique linkages
Journal of Combinatorial Theory Series B
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Planarity Allowing Few Error Vertices in Linear Time
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Obtaining a planar graph by vertex deletion
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Graph Minors. XXII. Irrelevant vertices in linkage problems
Journal of Combinatorial Theory Series B
Linkless and flat embeddings in 3-space and the unknot problem
Proceedings of the twenty-sixth annual symposium on Computational geometry
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
The disjoint paths problem: algorithm and structure
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
A simpler algorithm and shorter proof for the graph minor decomposition
Proceedings of the forty-third annual 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
Tight bounds for linkages in planar graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
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
Planar disjoint-paths completion
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
The structure of graphs with a vital linkage of order 2
Journal of Graph Theory
Effective computation of immersion obstructions for unions of graph classes
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
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At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful theorem which describes the structure of graphs excluding a fixed minor. This result is used to prove Wagner's conjecture and provide a polynomial time algorithm for the disjoint paths problem when the number of the terminals is fixed (i.e, the Graph Minor Algorithm). However, both results require the full power of the Graph Minor Theory, i.e, the structure theorem. In this paper, we show that this is not true in the latter case. Namely, we provide a new and much simpler proof of the correctness of the Graph Minor Algorithm. Specifically, we prove the "Unique Linkage Theorem" without using Graph Minors structure theorem. The new argument, in addition to being simpler, is much shorter, cutting the proof by at least 200 pages. We also give a new full proof of correctness of an algorithm for the well-known edge-disjoint paths problem when the number of the terminals is fixed, which is at most 25 pages long.