For any set Ω of non-negative integers such that , we consider a random Ω-k-tree G that is uniformly selected from all connected k-trees of (n + k) vertices such that the number of (k + 1)-cliques that contain any fixed k-clique belongs to Ω. We prove that G, scaled by where H is the kth harmonic number and σ > 0, converges to the continuum random tree . Furthermore, we prove local convergence of the random Ω-k-tree to an infinite but locally finite random Ω-k-tree G.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6686707 | PMC |
| http://dx.doi.org/10.1002/rsa.20802 | DOI Listing |
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