Brightwell, Graham
Overview
Works:  21 works in 29 publications in 1 language and 242 library holdings 

Roles:  Author 
Classifications:  QA164, 511.6 
Publication Timeline
.
Most widely held works by
Graham Brightwell
Combinatorics and probability : celebrating Béla Bollabás's 60th birthday(
Book
)
8 editions published in 2007 in English and held by 155 WorldCat member libraries worldwide
8 editions published in 2007 in English and held by 155 WorldCat member libraries worldwide
The structure of random discrete spacetime by
Graham Brightwell(
Book
)
1 edition published in 1990 in English and held by 75 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 75 WorldCat member libraries worldwide
Linear extensions of partially ordered sets by
Graham Brightwell(
Book
)
2 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1987 in English and held by 3 WorldCat member libraries worldwide
Special issue on Ramsey theory(
Book
)
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
Counting linear extensions is #Pcomplete by
Graham Brightwell(
Book
)
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Special issue in honour of Tom Trotter on his 65th birthday : papers from "New directions in algorithms, combinatorics and
optimization"(
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
Consultancy report by
Graham Brightwell(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Special issue in honour of Béla Bollobás on his 60th birthday(
Book
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
New directions in algorithms, combinatorics and optimization : papers dedicated to Tom Trotter on the occasion of his 65th
birthday(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
A second threshold for the hardcore model on a Bethe lattice by
Graham Brightwell(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
We determine the approximate value of a critical activity for the hardcore model on the Bethe lattice, which determines whether the unique simple invariant Gibbs measure is extremal. This “recovery threshold” turns out to be different both from the threshold for unique Gibbs measure and (in contrast to the Ising model) from the threshold for recovery of root information purely from statistical information about distant sites
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
We determine the approximate value of a critical activity for the hardcore model on the Bethe lattice, which determines whether the unique simple invariant Gibbs measure is extremal. This “recovery threshold” turns out to be different both from the threshold for unique Gibbs measure and (in contrast to the Ising model) from the threshold for recovery of root information purely from statistical information about distant sites
Submodular percolation by
Graham Brightwell(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
Graph homomorphisms and long range action by
Graham Brightwell(
)
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
On external subgraphs of a random graph by
Graham Brightwell(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
Held in New Orleans, LA, January 79, 2007. This symposium was sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
Held in New Orleans, LA, January 79, 2007. This symposium was sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics
On extremal subgraphs of random graphs by
Graham Brightwell(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
Let Kl denote the complete graph on vertices. We prove that there is a constant c = c(l) > 0, such that whenever p >= n(c), with probability tending to 1 when n goes to infinity, every maximum Klfree subgraph of the binomial random graph G(n,p) is (l1)partite. This answers a question of Babai, Simonovits and Spencer [3]. The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with M edges, where M >> n, is nearly unique. More precisely, given a maximum cut C of G(n,m), we can obtain all maximum cuts by moving at most O (root n(3/)M) vertices between the parts of C
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
Let Kl denote the complete graph on vertices. We prove that there is a constant c = c(l) > 0, such that whenever p >= n(c), with probability tending to 1 when n goes to infinity, every maximum Klfree subgraph of the binomial random graph G(n,p) is (l1)partite. This answers a question of Babai, Simonovits and Spencer [3]. The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with M edges, where M >> n, is nearly unique. More precisely, given a maximum cut C of G(n,m), we can obtain all maximum cuts by moving at most O (root n(3/)M) vertices between the parts of C
Partially ordered sets by
Graham Brightwell(
)
1 edition published in 2000 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 0 WorldCat member libraries worldwide
Orderinvariant measures on fixed causal sets by
Graham Brightwell(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the ordertype of the natural numbers  we call such a linear extension a {\em natural extension}. We study probability measures on the set of natural extensions of a causal set, especially those measures having the property of {\em orderinvariance}: if we condition on the set of the bottom k elements of the natural extension, each possible ordering among these k elements is equally likely. We give sufficient conditions for the existence and uniqueness of an orderinvariant measure on the set of natural extensions of a causal set
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the ordertype of the natural numbers  we call such a linear extension a {\em natural extension}. We study probability measures on the set of natural extensions of a causal set, especially those measures having the property of {\em orderinvariance}: if we condition on the set of the bottom k elements of the natural extension, each possible ordering among these k elements is equally likely. We give sufficient conditions for the existence and uniqueness of an orderinvariant measure on the set of natural extensions of a causal set
A second threshold for the hardcore model on a Bethe lattice by
Graham Brightwell(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
We determine the approximate value of a critical activity for the hardcore model on the Bethe lattice, which determines whether the unique simple invariant Gibbs measure is extremal. This “recovery threshold” turns out to be different both from the threshold for unique Gibbs measure and (in contrast to the Ising model) from the threshold for recovery of root information purely from statistical information about distant sites
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
We determine the approximate value of a critical activity for the hardcore model on the Bethe lattice, which determines whether the unique simple invariant Gibbs measure is extremal. This “recovery threshold” turns out to be different both from the threshold for unique Gibbs measure and (in contrast to the Ising model) from the threshold for recovery of root information purely from statistical information about distant sites
Extremal subgraphs of random graphs: an extended version by
Graham Brightwell(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
We prove that there is a constant $c >0$, such that whenever $p \ge n^{c}$, with probability tending to 1 when $n$ goes to infinity, every maximum trianglefree subgraph of the random graph $G_{n,p}$ is bipartite. This answers a question of Babai, Simonovits and Spencer (Journal of Graph Theory, 1990). The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with $M$ edges, where $M >> n$, is ``nearly unique''. More precisely, given a maximum cut $C$ of $G_{n,M}$, we can obtain all maximum cuts by moving at most $O(\sqrt{n^3/M})$ vertices between the parts of $C$
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
We prove that there is a constant $c >0$, such that whenever $p \ge n^{c}$, with probability tending to 1 when $n$ goes to infinity, every maximum trianglefree subgraph of the random graph $G_{n,p}$ is bipartite. This answers a question of Babai, Simonovits and Spencer (Journal of Graph Theory, 1990). The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with $M$ edges, where $M >> n$, is ``nearly unique''. More precisely, given a maximum cut $C$ of $G_{n,M}$, we can obtain all maximum cuts by moving at most $O(\sqrt{n^3/M})$ vertices between the parts of $C$
Random colorings of a cayley tree by
Graham Brightwell(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This volume is a collection of survey papers in combinatorics that have grown out of lectures given in the workshop on Probabilistic Combinatorics at the Paul Erdös Summer Research Center in Mathematics in Budapest. The papers, reflecting the many facets of modernday combinatorics, will be appreciated by specialists and general mathematicians alike: assuming relatively little background, each paper gives a quick introduction to an active area, enabling the reader to learn about the fundamental results and appreciate some of the latest developments. An important feature of the articles, very much in the spirit of Erdös, is the abundance of open problems
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This volume is a collection of survey papers in combinatorics that have grown out of lectures given in the workshop on Probabilistic Combinatorics at the Paul Erdös Summer Research Center in Mathematics in Budapest. The papers, reflecting the many facets of modernday combinatorics, will be appreciated by specialists and general mathematicians alike: assuming relatively little background, each paper gives a quick introduction to an active area, enabling the reader to learn about the fundamental results and appreciate some of the latest developments. An important feature of the articles, very much in the spirit of Erdös, is the abundance of open problems
Note on counting Eulerian circuits by
Graham Brightwell(
)
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P
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Brightwell, Graham R.
Brightwell, Graham Richard.
Graham Brightwell Mathematician
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