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Graph Minors
For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G byExpand
Graph Minors .XIII. The Disjoint Paths Problem
An algorithm, which for fixed k ≥ 0 has running time O (| V(G) | 3 ), to solve the following problem: given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs. Expand
The Complexity of Multiterminal Cuts
It is shown that the problem becomes NP-hard as soon as $k=3$, but can be solved in polynomial time for planar graphs for any fixed $k$, if the planar problem is NP- hard, however, if £k$ is not fixed. Expand
Decomposition of regular matroids
  • P. Seymour
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 June 1980
Abstract It is proved that every regular matroid may be constructed by piecing together graphic and cographic matroids and copies of a certain 10-element matroid.
Call routing and the ratcatcher
It follows that branch-width is polynomially computable for planar graphs—that too is NP-hard for general graphs. Expand
Graph Minors. II. Algorithmic Aspects of Tree-Width
We introduce an invariant of graphs called the tree-width, and use it to obtain a polynomially bounded algorithm to test if a graph has a subgraph contractible to H, where H is any fixed planarExpand
Quickly Excluding a Planar Graph
A much better bound is proved on the tree-width of planar graphs with no minor isomorphic to a g × g grid and this is the best known bound. Expand
Approximating clique-width and branch-width
A polynomial-time algorithm to approximate the branch-width of certain symmetric sub-modular functions, and gives two applications to graph "clique-width" and the area of matroid branch- width. Expand
The Strong Perfect Graph Theorem
A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle ofExpand
Graph minors. X. Obstructions to tree-decomposition
The obstructions to the existence of a graph are studied to find a minimax formula relating tree-width with the largest such obstructions and a “tree-decomposition” of the graph into pieces corresponding with the obstructions. Expand