{
  "annotation_id": "e7447963-d52a-46a6-89c1-b88af2426140",
  "date_created": "2026-02-17T05:53:04.518000Z",
  "date_modified": "2026-02-17T05:53:04.518000Z",
  "file_hash": "28f28fc56a3987e21f74e86071a64f15fdebaac4d9fcec081f744c9978e723b3",
  "private": false,
  "record": {
    "abstract": "In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vre\\\u0027cica and \\v{Z}ivaljevi\\\u0027c on cycle-free chessboard complexes (that is, multipath complexes of complete digraphs). In particular, we show that bidirectional path graphs are homotopic to spheres and that, in analogy with cycle-free chessboard complexes, multipath complexes of bidirectional polygonal digraphs are highly connected. Using a Mayer-Vietoris spectral sequence, we provide a computation of the associated homology groups. We study T-operations on graphs, and show that this corresponds to taking suspensions of multipath complexes. We further discuss (non) shellability properties of such complexes, and present new open questions.",
    "arxiv_id": "2601.05670",
    "authors": [
      "Luigi Caputi",
      "Carlo Collari",
      "Jason P. Smith"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Multipath complexes of bidirectional polygonal digraphs",
    "url": "https://arxiv.org/abs/2601.05670",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1330d40f-a175-41b2-9375-4b32d450151c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}