TY - JOUR

T1 - Large complete minors in random subgraphs

AU - Erde, Joshua

AU - Kang, Mihyun

AU - Krivelevich, Michael

N1 - Publisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85097267514&partnerID=8YFLogxK

U2 - 10.1017/S0963548320000607

DO - 10.1017/S0963548320000607

M3 - מאמר

AN - SCOPUS:85097267514

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

ER -