On Random Intersection Graphs: The Subgraph Problem
Combinatorics, Probability and Computing
The vertex degree distribution of random intersection graphs
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
The cover time of sparse random graphs
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Large independent sets in general random intersection graphs
Theoretical Computer Science
Combinatorial properties for efficient communication in distributed networks with local interactions
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
On the existence of hamiltonian cycles in random intersection graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Expander properties and the cover time of random intersection graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Consider a universal set ${\cal M}$ and a vertex set V and suppose that to each vertex in V we assign independently a subset of ${\cal M}$ chosen at random according to some probability distribution over subsets of ${\cal M}$. By connecting two vertices if their assigned subsets have elements in common, we get a random instance of a random intersection graphs model. In this work, we overview some results concerning the existence and efficient construction of Hamilton cycles in random intersection graph models. In particular, we present and discuss results concerning two special cases where the assigned subsets to the vertices are formed by (a) choosing each element of ${\cal M}$ independently with probability p and (b) selecting uniformly at random a subset of fixed cardinality.