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arXiv · 2301.04800

Minimum Weight Random Graphs with Edge Constraints

Ghurumuruhan Ganesan
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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 ${\mathbb{Z}^d}$ and employ martingale difference techniques to describe the behaviour of the scaled minimum weight in terms of the edge constraint.

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Ghurumuruhan Ganesan. 2023-01-12. Minimum Weight Random Graphs with Edge Constraints. https://arxiv.org/abs/2301.04800

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