Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Easy problems for tree-decomposable graphs
Journal of Algorithms
Sequential and parallel algorithms to find a K5 minor
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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We present a linear time algorithm which determines whether an input graph contains K5 as aminor and outputs a K5-model if the input graph contains one. If the input graph has no K5-minor then the algorithm constructs a tree decomposition such that each node of the tree corresponds to a planar graph or a graph with eight vertices. Such a decomposition can be used to obtain algorithms to solve various optimization problems in linear time. For example, we present a linear time algorithm for finding an O(√n) seperator and a linear time algorithm for solving k-realisation on graphs without a K5-minor. Our algorithm will also be used, in a separate paper, as a key subroutine in a nearly linear time algorithm to test for the existence of an H-minor for any fixed H.