Minimum Weight Random Graphs with Edge Constraints
Abstract
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on n vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation estimates for the minimum weight of subtrees with a given number of edges. Next we analyze edge constrained minimum weight paths in the integer lattice Zd and employ martingale difference techniques to describe the behaviour of the scaled minimum weight in terms of the edge constraint.
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