The cover time of cartesian product graphs

Authors:
Mohammed Abdullah;Colin Cooper;Tomasz Radzik
Affiliations:
Department of Computer Science, King's College London;Department of Computer Science, King's College London;Department of Computer Science, King's College London
Venue:
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Year:
2010

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Abstract

Let P = G□H be the cartesian product of graphs G, H. We relate the cover time COV[P] of P to the cover times of its factors. When one of the factors is in some sense larger than the other, its cover time dominates, and can become of the same order as the cover time of the product as a whole. Our main theorem effectively gives conditions for when this holds. The probabilistic technique which we introduce, based on the blanket time, is more general and may be of independent interest, as might some of our lemmas.