Abstract
Let G be a given graph (modeling a communication network) which we assume suffers from static edge faults: That is we let each edge of G be present independently with probability p (or absent with fault probability f = 1-p). In particular we are interested in robustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree d.
Here we deal with expansion properties of faulty random regular graphs and show: For d ≥ 42, fixed and p = κ/d, κ ≥ 20, a random regular graph with fault probability f = 1 - p contains a linear-sized subgraph which is an expander almost surely. This subgraph can be found by a simple linear-time algorithm.
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© 1998 Springer-Verlag Berlin Heidelberg
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Goerdt, A. (1998). Random Regular Graphs with Edge Faults: Expansion through Cores. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_24
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DOI: https://doi.org/10.1007/3-540-49381-6_24
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