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

- Paul D. Seymour, Robin Thomas
- J. Comb. Theory, Ser. B
- 1993

The tree-width of a graph G is the minimum k such that G may be decomposed into a “treestructure” of pieces each with at most k + 1 vertices. We prove that this equals the maximum k such that there is a collection of connected subgraphs, pairwise intersecting or adjacent, such that no set of ≤ k vertices meets all of them. A corollary is an analogue of… (More)

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

- Neil Robertson, Paul D. Seymour, Robin Thomas
- Combinatorica
- 1993

In 1943, Hadwiger made the conjecture that every loopless graph not contractible to the complete graph on t+1 vertices is t-colourable. When t ≤ 3 this is easy, and when t = 4, Wagner’s theorem of 1937 shows the conjecture to be equivalent to the four-colour conjecture (the 4CC). However, when t ≥ 5 it has remained open. Here we show that when t = 5 it is… (More)

- Thor Johnson, Neil Robertson, Paul D. Seymour, Robin Thomas
- J. Comb. Theory, Ser. B
- 2001

* Partially supported by NSF under Grant No. DMS-9701598. † Research partially supported by NSF under Grant No. DMS-9401981 and by DIMACS Center, Rutgers University, New Brunswick, NJ 08903. ‡ Partially supported by ONR under Contract No. N00014-97-1-0512. §Partially supported by NSF under Grant No. DMS-9623031, by NSA under Contract No. MDA904-98-1-0517,… (More)

- Noga Alon, Paul D. Seymour, Robin Thomas
- STOC
- 1990

Let G be an n-vertex graph with nonnegative weights whose sum is 1 assigned to its vertices, and with no minor isomorphic to a given h-vertex graph H. We prove that there is a set X of no more than h3/2nl/2 vertices of G whose deletion creates a graph in which the total weight of every connected component is at most 1/2. This extends significantly a… (More)

- Author Noga Alon, Paul Seymour, Robin Thomas
- 2007

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you… (More)

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

- Jirí Matousek, Robin Thomas
- Discrete Mathematics
- 1992

- Bruce A. Reed, Neil Robertson, Paul D. Seymour, Robin Thomas
- Combinatorica
- 1996

We prove a conjecture of Younger, that for every integer n ≥ 0 there exists an integer t ≥ 0 such that for every digraph G, either G has n vertex-disjoint directed circuits, or G can be made acyclic by deleting at most t vertices.