STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
2-Restricted extensions of partial embeddings of graphs
European Journal of Combinatorics - Special issue: Topological graph theory II
Every toroidal graph without adjacent triangles is (4, 1)*-choosable
Discrete Applied Mathematics
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Maximum matching in graphs with an excluded minor
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
ACO for Solving the Distributed Allocation of a Corporate Semantic Web
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
Approximating the crossing number of toroidal graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Linkless and flat embeddings in 3-space and the unknot problem
Proceedings of the twenty-sixth annual symposium on Computational geometry
Packet re-cycling: eliminating packet losses due to network failures
Hotnets-IX Proceedings of the 9th ACM SIGCOMM Workshop on Hot Topics in Networks
Testing planarity of partially embedded graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating the crossing number of graphs embeddable in any orientable surface
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Contractions of planar graphs in polynomial time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Determining edge expansion and other connectivity measures of graphs of bounded genus
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Errors in graph embedding algorithms
Journal of Computer and System Sciences
On graph crossing number and edge planarization
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Five-coloring graphs on the Klein bottle
Journal of Combinatorial Theory Series B
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
Matrix sparsification and nested dissection over arbitrary fields
Journal of the ACM (JACM)
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
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For an arbitrary fixed surface S, a linear time algorithm is presented that for a given graph G either finds an embedding of G in S or identifies a subgraph of G that is homeomorphic to a minimal forbidden subgraph for embeddability in S. A side result of the proof of the algorithm is that minimal forbidden subgraphs for embeddability in S cannot be arbitrarily large. This yields a constructive proof of the result of Robertson and Seymour that for each closed surface there are only finitely many minimal forbidden subgraphs. The results and methods of this paper can be used to solve more general embedding extension problems.