TY - JOUR
T1 - A random triadic process
AU - Korándi, Dániel
AU - Peled, Yuval
AU - Sudakov, Benny
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/11
Y1 - 2015/11
N2 - 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.
AB - 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.
KW - Differential equation method
KW - Random simplicial complexes
KW - Triadic process
UR - http://www.scopus.com/inward/record.url?scp=84947706405&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2015.06.028
DO - 10.1016/j.endm.2015.06.028
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AN - SCOPUS:84947706405
SN - 1571-0653
VL - 49
SP - 189
EP - 196
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -