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

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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Submitted on : Saturday, December 3, 2016 - 11:37:20 AM
Last modification on : Wednesday, December 7, 2016 - 1:01:42 AM
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  • HAL Id : ensl-01408160, version 1
  • ARXIV : 1605.05191

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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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