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Dismantling Sparse Random Graphs

Published online by Cambridge University Press:  01 March 2008

SVANTE JANSON  and
ANDREW THOMASON
SVANTE JANSON
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden (e-mail: svante.janson@math.uu.se, http://www.math.uu.se/~svante/)
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: a.g.thomason@dpmms.cam.ac.uk)
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Abstract

We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph have no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n → ∞, then the number in question is essentially the same for all values of k that satisfy both k → ∞ and k =o(n).

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 2 , March 2008 , pp. 259 - 264
Copyright
Copyright © Cambridge University Press 2007

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