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On Subgraph Sizes in Random Graphs

Published online by Cambridge University Press:  12 September 2008

Neil Calkin ,
Alan Frieze  and
Brendan D. McKay
Neil Calkin
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, U.S.A.
Alan Frieze
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, U.S.A.
Brendan D. McKay
Affiliation:
Department of Computer Science, Australian National University, Canberra, Australia
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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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 2 , June 1992 , pp. 123 - 134
Copyright
Copyright © Cambridge University Press 1992

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References

[1]Bollobás, B. (1985) Random Graphs. Academic Press, London.Google Scholar
[2]Knuth, D. E., Mothwani, R. and Pittel, B. (1990) Stable husbands. Random Structures and Algorithms 1, 1–14.Google Scholar