Vol. 10, No. 1, 2021

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Dense subgraphs of power-law random graphs

Denis O. Lazarev and Nikolay N. Kuzyurin

Vol. 10 (2021), No. 1, 1–11

The problem of finding a maximal dense subgraph of a power-law random graph G(n,α) is considered for every value of density c (0,1) and for every α (0,+). It is shown that in case α < 2 a maximal c-dense subgraph has size Θp(n1α2), in case α = 2 it is limited whp, and in case α > 2 it is whp less than 4 c.

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power-law random graph, Poissonian model, maximal dense subgraph, graph density, maximal dense subgraph of random graph.
Mathematical Subject Classification 2010
Primary: 05C42
Secondary: 05C69
Received: 27 December 2019
Revised: 21 July 2020
Accepted: 7 August 2020
Published: 16 January 2021
Denis O. Lazarev
Theoretical Computer Science Departement
Ivannikov Institute for System Programming of the RAS
Nikolay N. Kuzyurin
Theoretical Computer Science Departement
Ivannikov Institute for System Programming of the RAS