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Scaling limit of graph classes through split decomposition

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Abstract

We prove that Aldous' Brownian CRT is the scaling limit, with respect to the Gromov--Prokhorov topology, of uniform random graphs in each of the three following families of graphs: distance-hereditary graphs, $2$-connected distance-hereditary graphs and $3$-leaf power graphs. Our approach is based on the split decomposition and on analytic combinatorics.

Dates and versions

hal-03797906 , version 1 (04-10-2022)

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Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot. Scaling limit of graph classes through split decomposition. 2022. ⟨hal-03797906⟩
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