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
Outerplanar partitions of planar graphs
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
On chromatic sums and distributed resource allocation
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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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Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Computing vertex connectivity: new bounds from old techniques
Journal of Algorithms
Surfaces, tree-width, clique-minors, and partitions
Journal of Combinatorial Theory Series B
The extremal function for complete minors
Journal of Combinatorial Theory Series B
A characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
A short proof of Guenin's characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
Packing odd circuits in Eulerian graphs
Journal of Combinatorial Theory Series B
Efficient Approximation for Triangulation of Minimum Treewidth
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Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
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
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
Journal of Computer and System Sciences
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Edge partition of planar sraphs into two outerplanar graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Any 7-Chromatic Graphs Has K 7 Or K 4,4 As A Minor
Combinatorica
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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)
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On the connectivity of minimum and minimal counterexamples to Hadwiger's Conjecture
Journal of Combinatorial Theory Series B
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms Using Hierarchies of Semidefinite Programming Relaxations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Hardness and approximation of traffic grooming
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A theory of loss-leaders: making money by pricing below cost
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Finding shortest non-separating and non-contractible cycles for topologically embedded 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
Faster approximation schemes and parameterized algorithms on H-minor-free and odd-minor-free graphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Contraction decomposition in h-minor-free graphs and algorithmic applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Faster approximation schemes and parameterized algorithms on (odd-)H-minor-free graphs
Theoretical Computer Science
Cliques in odd-minor-free graphs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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We prove two structural decomposition theorems about graphs excluding a fixed odd minor H, and show how these theorems can be used to obtain approximation algorithms for several algorithmic problems in such graphs. Our decomposition results provide new structural insights into odd-H-minor-free graphs, on the one hand generalizing the central structural result from Graph Minor Theory, and on the other hand providing an algorithmic decomposition into two bounded-treewidth graphs, generalizing a similar result for minors. As one example of how these structural results conquer difficult problems, we obtain a polynomial-time 2-approximation for vertex coloring in odd-H-minor-free graphs, improving on the previous O(|V (H)|)-approximation for such graphs and generalizing the previous 2-approximation for H-minor-free graphs. The class of odd-H-minor-free graphs is a vast generalization of the well-studied H-minor-free graph families and includes, for example, all bipartite graphs plus a bounded number of apices. Odd-H-minor-free graphs are particularly interesting from a structural graph theory perspective because they break away from the sparsity of H-minor-free graphs, permitting a quadratic number of edges.