# 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…

## 3 Citations

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The Benjamini--Schramm convergence of random $k$-dimensional trees is proved, and a central limit theorem for the size of the largest $2$-connected component in random graphs from planar-like classes is recover in a probabilistic way.

### Graph limits of random unlabelled k-trees

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The main applications are Gromov–Hausdorff–Prokhorov and Benjamini–Schramm limits that describe their asymptotic geometric shape on a global and local scale as the number of (k + 1)-cliques tends to infinity.

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For a given combinatorial class $\mathcal{C}$ we study the class $\mathcal{G} = \mathrm{MSET}(\mathcal{C})$ satisfying the multiset construction, that is, any object in $\mathcal{G}$ is uniquely…

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