Abstract
The distance graph G(n, 2, 1) is a graph where vertices are identified with twoelement subsets of {1, 2,..., n}, and two vertices are connected by an edge whenever the corresponding subsets have exactly one common element. A random subgraph G p (n, 2, 1) in the Erd˝os–Rényi model is obtained by selecting each edge of G(n, 2, 1) with probability p independently of other edges. We find a lower bound on the independence number of the random subgraph G1/2(n, 2, 1).
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Original Russian Text © N.M. Derevyanko, S.G. Kiselev, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 4, pp. 3–15.
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Derevyanko, N.M., Kiselev, S.G. Independence Numbers of Random Subgraphs of Some Distance Graph. Probl Inf Transm 53, 307–318 (2017). https://doi.org/10.1134/S0032946017040019
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DOI: https://doi.org/10.1134/S0032946017040019