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A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a… (More)

- Louigi Addario-Berry, Nicolas Broutin, Gábor Lugosi
- 2009

We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been " contaminated, "… (More)

- Louigi Addario-Berry, Bruce Reed
- 2008

Given a branching random walk, let Mn be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{|Mn − EMn| > x}, under quite general conditions on the branching random walk. In particular , together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89–108], our results fully… (More)

- L Addario-Berry, N Broutin, C Goldschmidt, Louigi Addario-Berry, Nicolas Broutin, Christina Goldschmidt
- 2009

We consider the Erd˝ os–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn −4/3 , for some fixed λ ∈ R. We prove that the sequence of connected components of G(n, p), considered as metric spaces using the graph distance rescaled by n −1/3 , converges towards a sequence of continuous compact metric spaces. The result relies on a… (More)

- Louigi Addario-Berry, Svante Janson, Colin Mcdiarmid
- 2014

The spread of a connected graph G was introduced by Alon, Boppana and Spencer [1], and measures how tightly connected the graph is. It is defined as the maximum over all Lipschitz functions f on V (G) of the variance of f(X) when X is uniformly distributed on V (G). We investigate the spread for certain models of sparse random graph, in particular for… (More)

We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about α log n edges where α ≈ 3.5911 is the unique solution of the equation α log α − α = 1. This answers a question… (More)

In this paper, we present new structural results about the existence of a subgraph where the degrees of the vertices are pre-specified. Further, we use these results to prove a 16-edge-weighting version of a conjecture by Karo´nski, Luczak and Thoma-son, an asymptotic 2-edge-weighting version of the same conjecture, and a 7/8 version of Louigi's Conjecture.

A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted c v , is ev w(e). We show that the edges of every graph that does not contain a component isomorphic to K 2 can be weighted from the set {1,. .. , 30} such that in the resulting vertex-colouring of G, for every edge (u, v) of G, c u = c v .

Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task--in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be… (More)