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arXiv · 1911.10083

Depth First Exploration of a Configuration Model

Nathanaël Enriquez·Gabriel Faraud·Laurent Ménard·Nathan Noiry
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Abstract

We introduce an algorithm that constructs a random uniform graph with prescribed degree sequence together with a depth first exploration of it. In the so-called supercritical regime where the graph contains a giant component, we prove that the renormalized contour process of the Depth First Search Tree has a deterministic limiting profile that we identify. The proof goes through a detailed analysis of the evolution of the empirical degree distribution of unexplored vertices. This evolution is driven by an infinite system of differential equations which has a unique and explicit solution. As a byproduct, we deduce the existence of a macroscopic simple path and get a lower bound on its length.

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Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard, Nathan Noiry. 2019-11-22. Depth First Exploration of a Configuration Model. https://arxiv.org/abs/1911.10083

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