Simple and Efficient Greedy Algorithms for Hamilton Cycles in Random Intersection Graphs

In this work we consider the problem of finding Hamilton Cycles in graphs derived from the uniform random intersection graphs model Gn, m, p. In particular, (a) for the case m=nα, α>1 we give a result that allows us to apply (with the same probability of success) any algorithm that finds a Hamilton cycle with high probability in a Gn, k graph (i.e. a graph chosen equiprobably form the space of all graphs with k edges), (b) we give an expected polynomial time algorithm for the case p = constant and $m \leq \alpha {\sqrt{{n}\over {{\rm log}n}}}$ for some constant α, and (c) we show that the greedy approach still works well even in the case $m = o({{n}\over{{\rm log}n}})$ and p just above the connectivity threshold of Gn, m, p (found in [21]) by giving a greedy algorithm that finds a Hamilton cycle in those ranges of m, p with high probability.