References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On Percolation and the Bunkbed ConjecturePrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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panelAll.toggle();
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toggleList(panelAll.get(0).childNodes, panelAll);
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### 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: 000285718900007ScopusID: 2-s2.0-78650416664OAI: oai:DiVA.org:kth-29539DiVA: diva2:395423
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Funder

Knut and Alice Wallenberg Foundation
##### Note

QC 20110207Available from: 2011-02-07 Created: 2011-02-07 Last updated: 2011-02-07Bibliographically approved

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.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});