@article {IOPORT.05983378,
    author       = {Bloznelis, Mindaugas and Radavi\v{c}ius, Irmantas},
    title        = {A note on hamiltonicity of uniform random intersection graphs.},
    year         = {2011},
    journal      = {Lithuanian Mathematical Journal},
    volume       = {51},
    number       = {2},
    issn         = {0363-1672},
    pages        = {155-161},
    publisher    = {Springer, New York, NY},
    doi          = {10.1007/s10986-011-9115-7},
    abstract     = {Summary: We consider a collection of $n$ independent random subsets of $[m] = \{1, 2,\dots,m\}$ that are uniformly distributed in the class of subsets of size $d$, and call any two subsets adjacent whenever they intersect. This adjacency relation defines a graph called the uniform random intersection graph and denoted by $G_{ n,m,d }$. We fix $d = 2, 3,\dots$ and study when, as $n,m\rightarrow \infty$, the graph $G_{ n,m,d }$ contains a Hamilton cycle (the event denoted $G_{n,m,d}\in\cal H$). We show that $P(G_{n,m,d}\in\cal H) = o(1)$ for $d^{2} nm ^{-1}-\ln m-2\ln\ln m\rightarrow-\infty$ and $P(G_{n,m,d}\in\cal H) = 1-o(1)$ for $2nm^{-1}-\ln m-\ln\ln m\rightarrow +\infty $.},
    identifier   = {05983378},
}