NEGATIVE CORRELATION IN GRAPHS AND MATROIDS (2008)
Abstract. The following two conjectures arose in the work of Grimmett and Winkler, and Pemantle: the uniformly random forest F and the uniformly random connected subgraph C of a finite graph G have...
On the growth rate of minor-closed classes of graphs (2008)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
"Vegeu el resum a l'inici del document del fitxer adjunt."
We study the complexity of computing the coecients of three classical polynomials, namely the chromatic, ow and reliability polynomials of a graph. Each of these is a specialisation of the Tutte...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
John Michael Hammersley (1920-2004) (2006)
Grimmett, Geoffrey, Welsh, Dominic
In writing this biographical memoir of John Hammersley, we have tried to communicate something of the character of the person, and of the impact of his scientific achievements across lattice models...
Chromatic, Flow, and Reliability Polynomials: the Complexity of their Coefficients (2001)
Abstract We study the complexity of computing the coefficients of three classical polynomials, namely the chromatic, flow and reliability polynomials of a graph. Each of these is a specialisation of...
We study the complexity of computing the coefficients of three classical polynomials, namely the chromatic, flow and reliability polynomials of a graph. Each of these is a specialisation of the Tutte...
Arrangements, channel assignments and associated polynomials (1999)
The last decade has seen some massive developments in the theory of subspace arrangements and embeddings. Much of this has been concerned primarily with arrangements over the rational, real and...
Polynomial time randomised approximation schemes for the Tutte polynomial of dense graphs (1995)
Noga Alon, Alan Frieze, Dominic Welsh
The Tutte-Grothendieck polynomial T (G; x; y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x; y) plane give...
Noga Alon, Alan Frieze, Dominic Welsh
The Tutte-Grothendieck polynomial T (G; x; y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x; y) plane give...
Dominic Welsh Received, Noga Alon, Dominic Welsh
. The Tutte-Grothendieck polynomial T (G; x; y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x; y) plane give...
John Michael Hammersley, John Michael Hammersley, Geoffrey Grimmett, Dominic Welsh
John Hammersley was a pioneer amongst mathematicians who defied classification as