{
  "annotation_id": "6a944ceb-61b6-4141-9093-46de4d0f97bd",
  "date_created": "2026-02-17T05:53:12.445000Z",
  "date_modified": "2026-02-17T05:53:12.445000Z",
  "file_hash": "e3e89a892aac9fc39e43183884382d61cddf6792dec803e12563108b2cf7f023",
  "private": false,
  "record": {
    "abstract": "The celebrated formula of Otter \\emph{[Ann. of Math. (2) 49 (1948), 583--599]} asserts that the complete graph contains exponentially many non-isomorphic spanning trees. In this paper, we show that every connected almost regular graph with sufficiently large degree already contains exponentially many non-isomorphic spanning trees. Indeed, we prove a stronger statement: for every fixed $n$-vertex tree $T$, $$\n  \\Pr\\bigl[\\mathcal{T} \\simeq_{\\mathrm{iso}} T\\bigr] = e^{-\\Omega(n)}, $$ where $\\mathcal{T}$ is a uniformly random spanning tree of a connected $n$-vertex almost regular graph with sufficiently large degree. To prove this, we introduce a graph-theoretic variant of the classical balls--into--bins model, which may be of independent interest.",
    "arxiv_id": "2601.07740",
    "authors": [
      "Hyunwoo Lee"
    ],
    "categories": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Anticoncentration of random spanning trees in almost regular graphs",
    "url": "https://arxiv.org/abs/2601.07740",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cc438f52-2f61-41c3-a895-e55a0b4ec174",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}