Exact Expectations for Random Graphs and Assignments

Authors:
Henrik Eriksson;Kimmo Eriksson;Jonas Sjöstrand
Affiliations:
NADA, KTH, SE-100 44 Stockholm, Sweden (e-mail: henrik@nada.kth.se;IMA, Mälardalens högskola, Box 883, SE-721 23 Västerås, Sweden (e-mail: kimmo.eriksson@mdh.se);NADA, KTH, SE-100 44 Stockholm, Sweden (e-mail: jonass@nada.kth.se)
Venue:
Combinatorics, Probability and Computing
Year:
2003

Citing 2
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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 a bearing on the random assignment problem.