The Coupling Method for Inhomogeneous Random Intersection Graphs.

Katarzyna Rybarczyk

Abstract


We present new results concerning threshold functions for a wide family of random intersection graphs. To this end we improve and generalize  the coupling method introduced for random intersection graphs so that it may be used for a wider range of parameters. Using the new approach we are able to tighten the best known results concerning random intersection graphs and establish threshold functions for some monotone properties of inhomogeneous random intersection graphs. Considered properties are: $k$-connectivity, matching containment and hamiltonicity.

Keywords


Random intersection graph, Threshold function, Monotone property

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