Exact expectations for random graphs

Henrik Eriksson, Kimmo Eriksson, and Jonas Sjostrand

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


Abstract

For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest. For a random bipartite graph we give a formula for the expected time at which a k-assignment appears. This result has bearing upon the random assignment problem.


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