# Paul D. Seymour

- Publications
- Influence

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**public sources and our publisher partners.**Abstract We describe 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… Expand

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.

In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is asked for a minimum weight set of edges that separates each terminal from… Expand

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 planar… Expand

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 of… Expand

Suppose we expect there to bep(ab) phone calls between locationsa andb, all choices ofa, b from some setL of locations. We wish to design a network to optimally handle these calls. More precisely, a… Expand

We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric sub-modular functions, and give two applications.The first is to graph "clique-width." Clique-width is a… Expand

Abstract In an earlier paper, the first two authors proved that for any planar graph H , every graph with no minor isomorphic to H has bounded tree width; but the bound given there was enormous. Here… Expand

The tree-width of a graph G is the minimum k such that G may be decomposed into a "tree-structure" of pieces each with at most k + l vertices. We prove that this equals the maximum k such that there… Expand

Abstract 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… Expand