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Graph limits of random graphs from a subset of connected k-trees

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Abstract

For any set Ω of non-negative integers such that {0, 1} ⊆ Ω and {0, 1} = Ω, we consider a random Ω-k-tree G n,k that is uniformly selected from all connected k-trees of (n + k) vertices where the number of (k + 1)-cliques that contain any fixed k-clique belongs to Ω. We prove that G n,k , scaled by (kH k σ Ω)/(2 √ n) where H k is the k-th Harmonic number and σ Ω > 0, converges to the Continuum Random Tree Te. Furthermore, we prove the local convergence of the rooted random Ω-k-tree G • n,k to an infinite but locally finite random Ω-k-tree G ∞,k .
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Dates and versions

ensl-01408160 , version 1 (03-12-2016)

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Michael Drmota, Emma Yu, Benedikt Stufler. Graph limits of random graphs from a subset of connected k-trees. 2016. ⟨ensl-01408160⟩

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ENS-LYON INSMI UDL
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