{"paper":{"title":"Graph limits of random graphs from a subset of connected $k$-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Benedikt Stufler, Emma Yu Jin, Michael Drmota","submitted_at":"2016-05-17T14:40:13Z","abstract_excerpt":"For any set $\\Omega$ of non-negative integers such that $\\{0,1\\}\\subseteq \\Omega$ and $\\{0,1\\}\\ne \\Omega$, we consider a random $\\Omega$-$k$-tree ${\\sf G}_{n,k}$ 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 $\\Omega$. We prove that ${\\sf G}_{n,k}$, scaled by $(kH_{k}\\sigma_{\\Omega})/(2\\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\\sigma_{\\Omega}>0$, converges to the Continuum Random Tree $\\mathcal{T}_{{\\sf e}}$. Furthermore, we prove the local convergence of the rooted r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05191","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}