Louigi Addario-Berry

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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 Karoński, Luczak and Thomason, an asymptotic 2-edge-weighting version of the same conjecture, and a 7/8 version of Louigi’s Conjecture.
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)
This paper is concerned with evaluating the performance of the model and algorithm in 5 for detecting lateral gene transfers events. Using a Poisson process to describe arrival times of transfer events, a simulation is used to generate "synthetic" gene and species trees. An implementation of an efficient algorithm in 5 is used to estimate the minimum number(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 logn edges where α ≈ 3.5911 is the unique solution of the equation α logα − α = 1. This answers a question(More)
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)
An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a(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)
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)
" There is a big difference between a fair game and a game it's wise to play. "-Bertrand (1887b). 1 A brief history of ballot theorems 1.1 Discrete time ballot theorems We begin by sketching the development of the classical ballot theorem as it first appeared in the Comptes Rendus de l'Academie des Sciences. The statement that is fairly called the first(More)