A random triadic process

Dániel Korándi, Yuval Peled, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

Abstract

Given a random 3-uniform hypergraph H=H(n, p) on n vertices where each triple independently appears with probability p, consider the following graph process. We start with the star G0 on the same vertex set, containing all the edges incident to some vertex v0, and repeatedly add an edge xy if there is a vertex z such that xz and yz are already in the graph and xyz∈H. We say that the process propagates if all the edges are added to the graph eventually. In this paper we prove that the threshold probability for propagation is p=1/2√n. We also show that p=1/2√n is an upper bound for the threshold probability that a random 2-dimensional simplicial complex is simply-connected.

Original languageAmerican English
Pages (from-to)189-196
Number of pages8
JournalElectronic Notes in Discrete Mathematics
Volume49
DOIs
StatePublished - Nov 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

  • Differential equation method
  • Random simplicial complexes
  • Triadic process

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