On the limit of large girth graph sequences. (English) Zbl 1231.05259
Let \(d\geq2\) be given, and let \(\mu\) be an involution-invariant probability measure on the space of trees \(T\in {\mathcal T}_d\) with maximum degrees at most \(d\). Then \(\mu\) arises as the local limit of some sequence \(\{G_n\}_{n=1}^\infty\) of graphs with all degrees at most \(d\). This answers Question 3.3 of B. Bollobás and O. Riordan [“Sparse graphs: metrics and random models,” Random Struct. Algorithms 39, No.1, 1–38 (2011; Zbl 1223.05271)].
Reviewer: Willian G. Brown (Montreal)
MSC:
| 05C99 | Graph theory |
Citations:
Zbl 1223.05271References:
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