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- Graham R. Brightwell, Peter Winkler
- STOC
- 1991

We show that the problem of counting the number of linear extensions of a given partially ordered set is #P-complete. This settles a long-standing open question and contrssts with recent resultsâ€¦ (More)

- Graham R. Brightwell, William T. Trotter
- SIAM J. Discrete Math.
- 1993

With a convex polytope M in a, a partially ordered set PM is associated whose elements are the vertices, edges, and faces of M ordered by inclusion. This paper shows that the order dimension of P Mâ€¦ (More)

- Graham R. Brightwell, Peter Winkler
- J. Comb. Theory, Ser. B
- 2000

We model physical systems with \hard constraints" by the space Hom(G; H) of homomor-phisms from a locally nite graph G to a xed nite constraint graph H. Two homomorphisms are deemed to be adjacent ifâ€¦ (More)

- Graham R. Brightwell, Peter Winkler
- J. Comb. Theory, Ser. B
- 1999

We model physical systems with ``hard constraints'' by the space Hom(G, H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H. For any assignment * of positive realâ€¦ (More)

- Martin Anthony, Graham R. Brightwell, John Shawe-Taylor
- Discrete Applied Mathematics
- 1995

We say a function t in a set H of {0, 1}-valued functions defined on a set X is specified by S âŠ† X if the only function in H which agrees with t on S is t itself. The specification number of t is theâ€¦ (More)

- Peter Allen, Graham R. Brightwell, Jozef Skokan
- Combinatorica
- 2013

A celebrated result of ChvÃ¡tal, RÃ¶dl, SzemerÃ©di and Trotter states (in slightly weakened form) that, for every natural number Î”, there is a constant rÎ” such that, for any connected n-vertex graph Gâ€¦ (More)

- Graham R. Brightwell, Peter Winkler
- Random Struct. Algorithms
- 1990

For x and y vertices of a connected graph G, let TG(x, y) denote the expected time before a random walk starting from x reaches y. We determine, for each n > 0, the n-vertex graph G and vertices xâ€¦ (More)

- Graham R. Brightwell, William T. Trotter
- SIAM J. Discrete Math.
- 1997

This is a sequel to a previous paper entitled The Order Dimension of Convex Polytopes, by the same authors [SIAM J. Discrete Math., 6 (1993), pp. 230â€“245]. In that paper, we considered the poset PMâ€¦ (More)

- Graham R. Brightwell, Edward R. Scheinerman
- SIAM J. Discrete Math.
- 1993

- Noga Alon, Graham R. Brightwell, Hal A. Kierstead, Alexandr V. Kostochka, Peter Winkler
- J. Comb. Theory, Ser. B
- 2006

A k-majority tournament T on a finite vertex set V is defined by a set of 2k âˆ’ 1 linear orderings of V , with u â†’ v if and only if u lies above v in at least k of the orders. Motivated in part by theâ€¦ (More)