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Small Lifts of Expander Graphs are Expanding
, 2013
"... A klift of an nvertex basegraph G is a graph H on n × k vertices, where each vertex of G is replaced by k vertices and each edge (u, v) in G is replaced by a matching representing a bijection piuv so that the edges of H are of the form (u, i), (v, piuv(i)). H is a (uniformly) random lift of G if ..."
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if for every edge (u, v) the bijection piuv is chosen uniformly and independently at random. The main motivation for studying lifts has been understanding Ramanujan expander graphs via two key questions: Is a “typical ” lift of an expander graph also an expander; and how can we (efficiently) construct
Expander graphs in pure and applied mathematics
 Bull. Amer. Math. Soc. (N.S
"... Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number th ..."
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Cited by 30 (3 self)
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Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number
Expanding graphs and Ramsey numbers
, 1996
"... The generalized Ramsey number r(G; H) is investigated for H being a large order graph of bounded maximum degree. Giving a negative answer to a number of conjectures in generalized Ramsey theory it will be shown that for every nonbipartite graph G there is a function h(G; d) tending to infinity wi ..."
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The generalized Ramsey number r(G; H) is investigated for H being a large order graph of bounded maximum degree. Giving a negative answer to a number of conjectures in generalized Ramsey theory it will be shown that for every nonbipartite graph G there is a function h(G; d) tending to infinity
Fast Scramblers, Horizons and Expander Graphs
, 2014
"... We propose that local quantum systems defined on expander graphs provide a simple microscopic model for thermalization on quantum horizons. Such systems are automatically fast scramblers and are motivated from the membrane paradigm by a conformal transformation to the socalled optical metric. ..."
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Cited by 1 (0 self)
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We propose that local quantum systems defined on expander graphs provide a simple microscopic model for thermalization on quantum horizons. Such systems are automatically fast scramblers and are motivated from the membrane paradigm by a conformal transformation to the socalled optical metric.
EdgeDisjoint Paths in Expander Graphs
, 2000
"... Given a graph G = (17, E) and a set of t ¢ pairs of vertices in V, we are interested in finding for each pair (hi, b~), a path connecting ai to bi, such that the set of t ¢ paths so found is edgedisjoint. (For arbitrary graphs the problem is AfT~complete, although it is in 7 ~ if n is fixed.) We p ..."
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Cited by 27 (0 self)
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present a polynomial time randomized algorithm for finding edge disjoint paths in an rregular expander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large then all sets of n = g~(n/logn) pairs of vertices can be joined. This is within a constant factor
Cryptographic hash functions from expander graphs
"... We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two specific families of optimal expander graphs for provable hash function constructions: the families of Ramanujan graphs constructed by LubotzkyPhillipsSarnak and Pizer respec ..."
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Cited by 32 (4 self)
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We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two specific families of optimal expander graphs for provable hash function constructions: the families of Ramanujan graphs constructed by LubotzkyPhillipsSarnak and Pizer
Results 11  20
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1,337