k-Wise Independent Random Graphs

13 years 11 months ago

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We study the k-wise independent relaxation of the usual model G(N, p) of random graphs where, as in this model, N labeled vertices are ﬁxed and each edge is drawn with probability p, however, it is only required that the distribution of any subset of k edges is independent. This relaxation can be relevant in modeling phenomena where only k-wise independence is assumed to hold, and is also useful when the relevant graphs are so huge that handling G(N, p) graphs becomes infeasible, and cheaper random-looking distributions (such as k-wise independent ones) must be used instead. Unfortunately, many well-known properties of random graphs in G(N, p) are global, and it is thus not clear if they are guaranteed to hold in the k-wise independent case. We explore the properties of k-wise independent graphs by providing upper-bounds and lower-bounds on the amount of independence, k, required for maintaining the main properties of G(N, p) graphs: connectivity, Hamiltonicity, the connectivity-num...

Noga Alon, Asaf Nussboim

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