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- Neil Robertson, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 1995

- Neil Robertson, Paul D. Seymour
- J. Algorithms
- 1986

- Neil Robertson, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 1991

Roughly, a graph has small " tree-width " if it can be constructed by piecing small graphs together in a tree structure. Here we study the obstructions to the existence of such a tree structure. We find, for instance: (i) a minimax formula relating tree-width with the largest such obstructions (ii) an association between such obstructions and large grid… (More)

- Neil Robertson, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 1986

- Neil Robertson, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 2003

- Elias Dahlhaus, David S. Johnson, Christos H. Papadimitriou, Paul D. Seymour, Mihalis Yannakakis
- SIAM J. Comput.
- 1994

In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min-cut, max-flow problem, and can be solved in polynomial time. We show that the problem… (More)

- Neil Robertson, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 2004

We prove Wagner's conjecture, that for every infinite set of finite graphs, one of its members is isomorphic to a minor of another.

- Paul D. Seymour, Robin Thomas
- Combinatorica
- 1994

- Neil Robertson, Paul D. Seymour, Robin Thomas
- J. Comb. Theory, Ser. B
- 1994

- Sang-il Oum, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 2006

We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric submodular functions, and give two applications. The first is to graph " clique-width ". Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition… (More)