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math.CO2008
The longest minimum-weight path in a complete graph
Louigi Addario-Berry, Nicolas Broutin, Gabor Lugosi
We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables…
math.CO2008
The height of random binary unlabelled trees
Nicolas Broutin, Philippe Flajolet
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size is…