{
  "annotation_id": "4ed8e44d-130f-4023-b557-d92f6820ea00",
  "date_created": "2026-02-17T05:53:24.390000Z",
  "date_modified": "2026-02-17T05:53:24.390000Z",
  "file_hash": "9c8606fd20a3fe0333737e1b854445c4d6e85deea45eaf1050ec17c6dce25b8b",
  "private": false,
  "record": {
    "abstract": "A circuit double cover of a bridgeless graph is a collection of even subgraphs such that every edge is contained in exactly two subgraphs of the given collection. Such a circuit double cover describes an embedding of the corresponding graph onto a surface. In this paper, we investigate the well-known Orientable Strong Embedding Conjecture. This conjecture proposes that every bridgeless graph has a circuit double cover describing an embedding on an orientable surface. In a recent paper, we have proved that a 3-connected cubic planar graph G has exactly one orientable circuit double cover if and only if G is the dual graph of an Apollonian network. In this paper, we extend this result by demonstrating that this characterisation applies to any 3-connected planar graph, regardless of whether it is cubic.",
    "arxiv_id": "2601.10171",
    "authors": [
      "Meike Wei\u00df",
      "Reymond Akpanya",
      "Alice C. Niemeyer"
    ],
    "categories": [
      "math.CO",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On 3-Connected Planar Graphs with Unique Orientable Circuit Double Covers",
    "url": "https://arxiv.org/abs/2601.10171",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cee440a-4536-410e-8ddf-1891786fb516",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}