---
res:
  bibo_abstract:
  - "A famous conjecture by Itai and Zehavi states that, for every \U0001D451\r\n-vertex-connected
    graph \U0001D43A\r\n and every vertex \U0001D45F\r\n in \U0001D43A\r\n, there
    are \U0001D451\r\n spanning trees of \U0001D43A\r\n such that, for every vertex
    \U0001D463\r\n in \U0001D43A ∖{\U0001D45F}\r\n, the paths between \U0001D45F\r\n
    and \U0001D463\r\n in different trees are internally vertex-disjoint. We show
    that with high probability the Itai–Zehavi conjecture holds asymptotically for
    the Erdős–Rényi random graph \U0001D43A⁡(\U0001D45B,\U0001D45D)\r\n when \U0001D45B⁢\U0001D45D
    =\U0001D714⁡(log⁡\U0001D45B)\r\n and for random regular graphs \U0001D43A⁡(\U0001D45B,\U0001D451)\r\n
    when \U0001D451 =\U0001D714⁡(log⁡\U0001D45B)\r\n. Moreover, we essentially confirm
    the conjecture up to a constant factor for sparser random regular graphs. This
    answers a question of Draganić and Krivelevich positively. Our proof makes use
    of recent developments on sprinkling techniques in random regular graphs.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Lawrence
      foaf_name: Hollom, Lawrence
      foaf_surname: Hollom
  - foaf_Person:
      foaf_givenName: Lyuben
      foaf_name: Lichev, Lyuben
      foaf_surname: Lichev
      foaf_workInfoHomepage: http://www.librecat.org/personId=9aa8388e-d003-11ee-8458-c4c1d7447977
  - foaf_Person:
      foaf_givenName: Adva
      foaf_name: Mond, Adva
      foaf_surname: Mond
  - foaf_Person:
      foaf_givenName: Julien
      foaf_name: Portier, Julien
      foaf_surname: Portier
  - foaf_Person:
      foaf_givenName: Yiting
      foaf_name: Wang, Yiting
      foaf_surname: Wang
      foaf_workInfoHomepage: http://www.librecat.org/personId=1917d194-076e-11ed-97cd-837255f88785
  bibo_doi: 10.1002/rsa.70095
  bibo_issue: '2'
  bibo_volume: 69
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1042-9832
  - http://id.crossref.org/issn/1098-2418
  dct_language: eng
  dct_publisher: Wiley@
  dct_title: Approximate Itai–Zehavi conjecture for random graphs@
...