---
res:
  bibo_abstract:
  - "Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing
    path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by
    switching some zero coordinate in vi to a one coordinate in vi+1.\r\nForm a random
    subgraph Qdp by retaining each edge in E(Qd) independently with probability p.
    We show that there is a phase transition with respect to the length of a longest
    increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then
    there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length
    at most δd. On the other hand, when α>e, whp there is a path of length d−2 in
    Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the
    all-zero and all-one vertices percolate or not.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Anastos, Michael
      foaf_surname: Anastos
      foaf_workInfoHomepage: http://www.librecat.org/personId=0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  - foaf_Person:
      foaf_givenName: Sahar
      foaf_name: Diskin, Sahar
      foaf_surname: Diskin
  - foaf_Person:
      foaf_givenName: Dor
      foaf_name: Elboim, Dor
      foaf_surname: Elboim
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Krivelevich, Michael
      foaf_surname: Krivelevich
  bibo_doi: 10.1214/24-ECP639
  bibo_volume: 29
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001356019700001
  dct_isPartOf:
  - http://id.crossref.org/issn/1083-589X
  dct_language: eng
  dct_publisher: Duke University Press@
  dct_title: Climbing up a random subgraph of the hypercube@
...