Domingos Dellamonica

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In this paper we determine the local and global resilience of random graphs Gn,p (p n−1) with respect to the property of containing a cycle of length at least (1 − α)n. Roughly speaking, given α > 0, we determine the smallest rg(G,α) with the property that almost surely every subgraph of G = Gn,p having more than rg(G,α)|E(G)| edges contains a cycle of(More)
Given a graph G, the size-Ramsey number r̂(G) is the minimum number m for which there exists a graph F on m edges such that any two-coloring of the edges of F admits a monochromatic copy of G. In 1983, J. Beck introduced an invariant β(·) for trees and showed that r̂(T ) = Ω(β(T )). Moreover he conjectured that r̂(T ) = Θ(β(T )). We settle this conjecture(More)
We give a polynomial time randomized algorithm that, on receiving as input a pair (H,G) of n-vertex graphs, searches for an embedding of H into G. If H has bounded maximum degree and G is suitably dense and pseudorandom, then the algorithm succeeds with high probability. Our algorithm proves that, for every integer d ≥ 3 and a large enough constant C = Cd,(More)
We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems.(More)
The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions(More)
An (n, d)-expander is a graph G = (V,E) such that for every X ⊆ V with |X| ≤ 2n− 2 we have |ΓG(X)| ≥ (d + 1)|X|. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)-expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm(More)
We prove that asymptotically (as <i>n</i> &#8594; &#8734;) almost all graphs with <i>n</i> vertices and 10<i>d n</i><sup>2</sup>--1/2<i>d</i> log <sup>1/<i>d</i></sup> <i>n</i> edges are universal with respect to the family of all graphs with maximum degree bounded by <i>d.</i> Moreover, we provide a polynomial time, deterministic embedding algorithm to(More)
For all fixed trees T and any graph G we derive a counting formula for the number N̂T (G) of homomorphisms from T to G in terms of the degree sequence of G. As a consequence we obtain that any n-vertex graph G with edge density p = p(n) n−1/(t−2), which contains at most (1 + o(1))pt−1nt copies of some fixed tree T with t ≥ 3 vertices must be almost regular,(More)