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On Percolation and the Bunkbed Conjecture
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
2011 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 20, no 1, 103-117 p.Article in journal (Refereed) Published
Abstract [en]

We study a problem on edge percolation on product graphs G x K-2. Here G is any finite graph and K-2 consists of two vertices {0, 1} connected by an edge. Every edge in G x K-2 is present with probability p independent of other edges. The bunkbed conjecture states that for all G and p, the probability that (u, 0) is in the same component as (v, 0) is greater than or equal to the probability that (u, 0) is in the same component as (v, 1) for every pair of vertices u, v is an element of G. We generalize this conjecture and formulate and prove similar statements for randomly directed graphs. The methods lead to a proof of the original conjecture for special classes of graphs G, in particular outerplanar graphs.

Place, publisher, year, edition, pages
2011. Vol. 20, no 1, 103-117 p.
Keyword [en]
RANDOM-WALKS, GRAPHS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-29539DOI: 10.1017/S0963548309990666ISI: 000285718900007Scopus ID: 2-s2.0-78650416664OAI: oai:DiVA.org:kth-29539DiVA: diva2:395423
Funder
Knut and Alice Wallenberg Foundation
Note
QC 20110207Available from: 2011-02-07 Created: 2011-02-07 Last updated: 2017-12-11Bibliographically approved

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Linusson, Svante

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