Work

Increasing paths in random temporal graphs

Year: 2024

Type: article

Abstract: We consider random temporal graphs, a version of the classical Erdős–Rényi 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 logn. 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.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2097

Authors: Nicolas Broutin, Nina Kamčev, Gábor Lugosi

Institutions: Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation, University of Zagreb, Institució Catalana de Recerca i Estudis Avançats

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundación BBVA, Ministerio de Economía y Competitividad, Banco Bilbao Vizcaya Argentaria

Award: G6756599787