A separator theorem for graphs of bounded genus
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Approximation algorithms for NP-complete problems on planar graphs
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Graph minors. XI.: circuits on a surface
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Separating and nonseparating disjoint homotopic cycles in graph embeddings
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All structured programs have small tree width and good register allocation
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Zero knowledge and the chromatic number
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A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
SIAM Journal on Discrete Mathematics
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
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Light spanners and approximate TSP in weighted graphs with forbidden minors
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Graph minors. XVI. excluding a non-planar graph
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Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence of local treewidth and linear local treewidth and its algorithmic applications
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Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
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Bidimensional Parameters and Local Treewidth
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Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A linear-time approximation scheme for planar weighted TSP
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)
Spectral Partitioning, Eigenvalue Bounds, and Circle Packings for Graphs of Bounded Genus
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The Bidimensional Theory of Bounded-Genus Graphs
SIAM Journal on Discrete Mathematics
A subset spanner for Planar graphs,: with application to subset TSP
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Fast subexponential algorithm for non-local problems on graphs of bounded genus
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Approximation schemes for minimum 2-connected spanning subgraphs in weighted planar graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Catalan structures and dynamic programming in H-minor-free graphs
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Testing contractibility in planar rips complexes
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Homology flows, cohomology cuts
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Minimum cuts and shortest homologous cycles
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Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth Graphs
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
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A shorter proof of the graph minor algorithm: the unique linkage theorem
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Decomposition, approximation, and coloring of odd-minor-free graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Contraction decomposition in h-minor-free graphs and algorithmic applications
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Shortest non-trivial cycles in directed surface graphs
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Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
An efficient polynomial-time approximation scheme for Steiner forest in planar graphs
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Spanning closed walks and TSP in 3-connected planar graphs
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Global minimum cuts in surface embedded graphs
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Faster approximation schemes and parameterized algorithms on (odd-)H-minor-free graphs
Theoretical Computer Science
The asymmetric traveling salesman problem on graphs with bounded genus
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Prize-collecting Steiner problems on planar graphs
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Minimum cuts and shortest non-separating cycles via homology covers
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Catalan structures and dynamic programming in H-minor-free graphs
Journal of Computer and System Sciences
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MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
On the excluded minor structure theorem for graphs of large tree-width
Journal of Combinatorial Theory Series B
The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs
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Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound depends on k). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained in [Bak94, Epp00, DDO+04, DHK05], and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs [Kle05]. Our decomposition result is a powerful tool for obtaining PTASs for contraction-closed problems (whose optimal solution only improves under contraction), a much more general class than minor-closed problems. We prove that any contraction-closed problem satisfying just a few simple conditions has a PTAS in bounded-genus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimum-weight c-edge-connected submultigraph on bounded-genus graphs, improving and generalizing previous algorithms of [GKP95, AGK+98, Kle05, Gri00, CGSZ04, BCGZ05]. We also highlight the only main difficulty in extending our results to general H-minor-free graphs.