On the limit of large girth graph sequences

2008/11/07 by Gábor Elek, Elek, Gabor · 2 citations
Computer Science · Mathematics · #05C99 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.0811.1149

openalex publication_date 2008/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any involution-invariant probability measure on the space of trees with maximum degrees at most d arises as the local limit of a convergent large girth graph sequence. This answers a question of Bollobas and Riordan.

Cited by

• Minor-excluded graphs and soficity
• On the trace of branching random walks

Related

• Graphical sequences and plane trees
• Treeable Graphings Are Local Limits of Finite Graphs
• Marked random graphs with given degree sequence: large deviations on the local topology
• Limits of Random Trees II
• Multipartite random graphs with given degrees: local limit, revisiting the giant, distances