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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)
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)
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)
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)
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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