Expander properties and the cover time of random intersection graphs

Authors:
S. Nikoletseas;C. Raptopoulos;P. G. Spirakis
Affiliations:
University of Patras, 26500 Patras, Greece and Computer Technology Institute, P.O. Box 1122, 26110 Patras, Greece;University of Patras, 26500 Patras, Greece and Computer Technology Institute, P.O. Box 1122, 26110 Patras, Greece;University of Patras, 26500 Patras, Greece and Computer Technology Institute, P.O. Box 1122, 26110 Patras, Greece
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We investigate important combinatorial and algorithmic properties of G"n","m","p random intersection graphs. In particular, we prove that with high probability (a) random intersection graphs are expanders, (b) random walks on such graphs are ''rapidly mixing'' (in particular they mix in logarithmic time) and (c) the cover time of random walks on such graphs is optimal (i.e. it is @Q(nlogn)). All results are proved for p very close to the connectivity threshold and for the interesting, non-trivial range where random intersection graphs differ from classical G"n","p random graphs.