Increasing paths in random temporal graphs

Nicolas Broutin; Nina Kamčev; Gabor Lugosi

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arXiv · 2306.11401

Increasing paths in random temporal graphs

Nicolas Broutin·Nina Kamčev·Gabor Lugosi

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Abstract

We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time stamps. We study the asymptotics for the distances in such graphs, mostly in the regime of interest where np is of order log n. We establish the first order asymptotics for the lengths of increasing paths: the lengths of the shortest and longest paths between typical vertices, the maxima of these lengths from a given vertex, as well as the maxima between any two vertices; this covers the (temporal) diameter.

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BibTeX RIS

Nicolas Broutin, Nina Kamčev, Gabor Lugosi. 2023-06-20. Increasing paths in random temporal graphs. https://arxiv.org/abs/2306.11401

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