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Random Graph Coverings I: General Theory and Graph Connectivity

✍ Scribed by Alon Amit; Nathan Linial


Publisher
Springer-Verlag
Year
2002
Tongue
English
Weight
254 KB
Volume
22
Category
Article
ISSN
0209-9683

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πŸ“œ SIMILAR VOLUMES


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## Abstract A graph is locally connected if for each vertex Ξ½ of degree __≧2__, the subgraph induced by the vertices adjacent to Ξ½ is connected. In this paper we establish a sharp threshold function for local connectivity. Specifically, if the probability of an edge of a labeled graph of order __n_

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We prove that, in a random graph with n vertices and N = cn log n edges, the subgraph generated by a set of all vertices of degree at least k + 1 is k-leaf connected for c > f . A threshold function for k-leaf connectivity is also found. ## 1. MAIN RESULTS Let G = (V(G),E(G)) be a graph, where V (

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While it is straightforward to simulate a very general class of random processes space-efficiently by non-unitary quantum computations (e.g., quantum computations that allow intermediate measurements to occur), it is not currently known to what extent restricting quantum computations to be unitary a