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Abstract
Let G be a graph of minimum degree at least k and let Gp be the random subgraph of G obtained by keeping each edge independently with probability p. We are interested in the size of the largest complete minor that Gp contains when p = (1 + ϵ)/k with ϵ > 0. We show that with high probability Gp contains a complete minor of order <![CDATA[ \tilde{\Omega}(\sqrt{k})[]>, where the hides a polylogarithmic factor. Furthermore, in the case where the order of G is also bounded above by a constant multiple of k, we show that this polylogarithmic term can be removed, giving a tight bound.
Original language  English 

Pages (fromto)  619630 
Number of pages  11 
Journal  Combinatorics, Probability & Computing 
Volume  30 
Issue number  4 
Early online date  Dec 2020 
DOIs  
Publication status  Published  10 Jun 2021 
ASJC Scopus subject areas
 Theoretical Computer Science
 Applied Mathematics
 Statistics and Probability
 Computational Theory and Mathematics
Fields of Expertise
 Information, Communication & Computing
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 1 Finished

FWF  Cores  Random Graphs: Cores, Colourings and Contagion
1/09/18 → 30/06/22
Project: Research project