  The construction of the random intersection graph model is based on a random
family of sets. Such structures, which are derived from intersections of sets,
appear in a natural manner in many applications. In this article we study the
problem of finding a Hamilton cycle in a random intersection graph. To this end
we analyse a classical algorithm for finding Hamilton cycles in random graphs
(algorithm HAM) and study its efficiency on graphs from a family of random
intersection graphs (denoted here by G(n,m,p)). We prove that the threshold
function for the property of HAM constructing a Hamilton cycle in G(n,m,p) is
the same as the threshold function for the minimum degree at least two. Until
now, known algorithms for finding Hamilton cycles in G(n,m,p) were designed to
work in very small ranges of parameters and, unlike HAM, used the structure of
the family of random sets.
