Graph limits of random graphs from a subset of connected k-treesReportar como inadecuado




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1 TU WIEN - Technical University of Vienna Vienna 2 ENS Lyon - École normale supérieure - Lyon

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 .

Keywords : partial k-trees Continuum Random Tree modified Galton-Watson tree





Autor: Michael Drmota - Emma Yu - Benedikt Stufler -

Fuente: https://hal.archives-ouvertes.fr/



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