Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Improved algorithms for graph four-connectivity
Journal of Computer and System Sciences
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Sequential and parallel algorithms to find a K5 minor
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Treewidth of Circular-Arc Graphs
SIAM Journal on Discrete Mathematics
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Treewidth for graphs with small chordality
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Depth-First Search and Kuratowski Subgraphs
Journal of the ACM (JACM)
A linear time algorithm for minimum fill-in and treewidth for distance hereditary graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Vertex Cover: Further Observations and Further Improvements
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Graph Theory With Applications
Graph Theory With Applications
Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free 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
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
MAX-CUT and containment relations in graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Algorithmic graph minor theory: improved grid minor bounds and wagner's contraction
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Note: max-cut and containment relations in graphs
Theoretical Computer Science
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We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K5-minor-free graphs and K3,3-minor-free graphs. Along the way, we present a polynomial-time algorithm to decompose H-minor-free graphs into planar graphs and graphs of treewidth at most cH (a constant dependent on H) using clique sums. This result has several applications in designing fully polynomial-time approximation schemes and fixed-parameter algorithms for many NP-complete problems on these graphs.