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- Louigi Addario-Berry, Maria Chudnovsky, Frédéric Havet, Bruce A. Reed, Paul D. Seymour
- J. Comb. Theory, Ser. B
- 2008

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)

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)

- L. Addario-Berry
- 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, B A Reed
- 2008

We prove an analogue of the classical ballot theorem that holds for any mean zero random walk with positive but finite variance. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are removed, our conclusions may no longer hold.

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, Robert E. L. Aldred, Ketan Dalal, Bruce A. Reed
- J. Comb. Theory, Ser. B
- 2005

We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton–Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, non-asymptotic distributional result for the case of uniformly random rooted labeled… (More)

- Louigi Addario-Berry, Nicolas Broutin, Gábor Lugosi
- Combinatorics, Probability & Computing
- 2010

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)

We consider a branching random walk for which the maximum position of a particle in the n'th generation, Rn, has zero speed on the linear scale: Rn/n → 0 as n → ∞. We further remove (" kill ") any particle whose displacement is negative, together with its entire descendence. The size Z of the set of un-killed particles is almost surely finite [26, 31]. In… (More)

- Louigi Addario-Berry, Ketan Dalal, Bruce A. Reed
- Discrete Applied Mathematics
- 2005

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.