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We adopt a utilitarian perspective on social choice, assuming that agents have (possibly latent) utility functions over some space of alternatives. For many reasons one might consider mechanisms, or <i>social choice functions</i>, that only have access to the ordinal rankings of alternatives by the individual agents rather than their utility functions. In… (More)

- Noga Alon, Simi Haber, Michael Krivelevich
- Electr. J. Comb.
- 2011

For graphs F and G an F-matching in G is a subgraph of G consisting of pairwise vertex disjoint copies of F. The number of F-matchings in G is denoted by s(F, G). We show that for every fixed positive integer m and every fixed tree F , the probability that s(F, T n) ≡ 0 (mod m), where T n is a random labeled tree with n vertices, tends to one exponentially… (More)

The first order language of graphs is a formal language in which one can express many properties of graphs — known as first order properties. The classic Zero-One law for random graphs states that if p is some constant probability then for every first order property the limiting probability of the binomial random graph G(n, p) having this property is either… (More)

- Itai Benjamini, Simi Haber, Michael Krivelevich, Eyal Lubetzky
- Random Struct. Algorithms
- 2008

The isoperimetric constant of a graph G on n vertices, i(G), is the minimum of |∂S| |S| , taken over all nonempty subsets S ⊂ V (G) of size at most n/2, where ∂S denotes the set of edges with precisely one end in S. A random graph process on n vertices, G(t), is a sequence of n 2 graphs, where G(0) is the edgeless graph on n vertices, and G(t) is the result… (More)

- Alan M. Frieze, Simi Haber
- Random Struct. Algorithms
- 2015

We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G = G δ≥3 n,m. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n 1+o(1)) time and… (More)

- Simi Haber, Michael Krivelevich
- Random Struct. Algorithms
- 2007

- Simi Haber, Saharon Shelah
- Fields of Logic and Computation II
- 2015

- Simi Haber, Michael Krivelevich
- Random Struct. Algorithms
- 2008

- Simi Haber, Saharon Shelah
- 2012

We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P , is there a language of graphs able to express P while obeying the zero-one law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey… (More)

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