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

@article{Drmota2019GraphLO,
  title={Graph limits of random graphs from a subset of connected k‐trees},
  author={Michael Drmota and Emma Yu Jin and Benedikt Stufler},
  journal={Random Structures \& Algorithms},
  year={2019},
  volume={55},
  pages={125 - 152}
}
For any set Ω of non‐negative integers such that {0,1}⊊Ω , we consider a random Ω‐k‐tree Gn,k 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 Gn,k, scaled by (kHkσΩ)/(2n) where Hk is the kth harmonic number and σΩ > 0, converges to the continuum random tree Te . Furthermore, we prove local convergence of the random Ω‐k‐tree Gn,k∘ to an infinite but locally finite random… 

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