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On Subgraph Sizes in Random Graphs

Neil Calkin, Alan Frieze, Brendan D. McKay

Source record

Source: Crossref

Published: Jun 1, 1992

DOI: 10.1017/s0963548300000146

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Source abstract

For a graph G with m edges let its Range of Subgraph Sizes (RSS) ρ( G ) = { t : G contains a vertex-induced subgraph with t edges}. G has a full RSS if ρ( G ) = {0, 1, …, m }. We establish the threshold for a random graph to have a full RSS and give tight bounds on the likely RSS of a dense random graph.

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On Subgraph Sizes in Random Graphs — Mathematical Frontier Network