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RSA
2006

Regular graphs whose subgraphs tend to be acyclic

12 years 1 months ago
Regular graphs whose subgraphs tend to be acyclic
Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , > 0 and any integer d 2, explicit or randomized constructions of d-regular graphs on n > n0( , ) vertices in which a random subgraph obtained by retaining each edge, randomly and independently, with probability = 1d-1 , is acyclic with probability at least 1 - . On the other hand we show that for any d-regular graph G on n > n1( , ) vertices, a random subgraph of G obtained by retaining each edge, randomly and independently, with probability = 1+ d-1 , does contain a cycle with probability at least 1-. The proofs combine probabilistic and combinatorial arguments, with number theoretic techniques.
Noga Alon, Eitan Bachmat
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2006
Where RSA
Authors Noga Alon, Eitan Bachmat
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