# Brightwell, Graham

Overview
Works: 21 works in 24 publications in 1 language and 227 library holdings QA164, 511/.6
Publication Timeline
1980 | |2010
Key
Publications by Graham Brightwell
Most widely held works by Graham Brightwell
Combinatorics and probability : celebrating Béla Bollabás's 60th birthday ( )
2 editions published in 2007 in English and held by 132 WorldCat member libraries worldwide
The structure of random discrete spacetime by Graham Brightwell ( Book )
1 edition published in 1990 in English and held by 64 WorldCat member libraries worldwide
Combinatorics and probability celebrating Béla Bollobás's 60th birthday ( Book )
2 editions published in 2007 in English and held by 6 WorldCat member libraries worldwide
Linear extensions of partially ordered sets by Graham Brightwell ( Book )
2 editions published in 1987 in Undetermined and 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
Counting linear extensions is #P-complete by Graham Brightwell ( Book )
1 edition published in 1990 in English and held by 2 WorldCat member libraries worldwide
Submodular percolation by Graham Brightwell ( )
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Note on counting Eulerian circuits by Graham Brightwell ( )
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P
A second threshold for the hard-core model on a Bethe lattice by Graham Brightwell ( )
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
We determine the approximate value of a critical activity for the hard-core 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
A second threshold for the hard-core model on a Bethe lattice by Graham Brightwell ( )
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
We determine the approximate value of a critical activity for the hard-core 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
Consultancy report by Graham Brightwell ( Book )
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Graph homomorphisms and long range action by Graham Brightwell ( )
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Order-invariant measures on fixed causal sets by Graham Brightwell ( )
1 edition published in 2009 in English and held by 1 WorldCat member library 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 order-type 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 order-invariance}: 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 order-invariant measure on the set of natural extensions of a causal set
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
On extremal subgraphs of random graphs by Graham Brightwell ( )
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Let K-l 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 K-l-free subgraph of the binomial random graph G(n,p) is (l-1)-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
Random colorings of a cayley tree by Graham Brightwell ( )
1 edition published in 2002 in English and held by 1 WorldCat member library 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 modern-day 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
Extremal subgraphs of random graphs: an extended version by Graham Brightwell ( )
1 edition published in 2009 in English and held by 1 WorldCat member library 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 triangle-free 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 $C$
Partially ordered sets by Graham Brightwell ( )
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Counting Eulerian circuits is #P-complete by Graham Brightwell ( )
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide

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Audience Level
 0 1 Kids General Special

Related Identities
Alternative Names
Brightwell, Graham R.
Brightwell, Graham Richard.
Languages
English (22)
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