The degree sequence of a random graph. I. The models
Random Structures & Algorithms
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
Sharp Threshold for Hamiltonicity of Random Geometric Graphs
SIAM Journal on Discrete Mathematics
Tail bounds for occupancy and the satisfiability threshold conjecture
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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
A guided tour in random intersection graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
| Hi-index | 5.23 |
Random Intersection Graphs, G"n","m","p, is a class of random graphs introduced in Karonski (1999) [7] where each of the n vertices chooses independently a random subset of a universal set of m elements. Each element of the universal sets is chosen independently by some vertex with probability p. Two vertices are joined by an edge iff their chosen element sets intersect. Given n, m so that m=@?n^@a@?, for any real @a different than one, we establish here, for the first time, a sharp threshold for the graph property ''Contains a Hamilton cycle''. Our proof involves new, nontrivial, coupling techniques that allow us to circumvent the edge dependencies in the random intersection graph model.