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  "path": "/abs/2603.02827v1",
  "publishedAt": "2026-03-04T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Sabine Cornelsen",
    "Jan Kratochvíl",
    "Miriam Münch",
    "Giacomo Ortali",
    "Alexandra Weinberger",
    "Alexander Wolff"
  ],
  "textContent": "**Authors:** Sabine Cornelsen, Jan Kratochvíl, Miriam Münch, Giacomo Ortali, Alexandra Weinberger, Alexander Wolff\n\nIn a {\\em grounded string representation} of a graph there is a horizontal line $\\ell$ and each vertex is represented as a simple curve below $\\ell$ with one end point on $\\ell$ such that two curves intersect if and only if the respective vertices are adjacent. A grounded string representation is a {\\em grounded L-reverseL-representation} if each vertex is represented by a 1-bend orthogonal polyline. It is a {\\em grounded L-representation} if in addition all curves are L-shaped. We show that every biconnected series-parallel graph without edges between the two vertices of a separation pair (i.e., {\\em transitive edges}) admits a grounded L-reverseL-representation if and only if it admits a grounded string representation. Moreover, we can test in linear time whether such a representation exists. We also construct a biconnected series-parallel graph without transitive edges that admits a grounded L-reverseL-representation, but no grounded L-representation.",
  "title": "Grounded String Representations of Series-Parallel Graphs without Transitive Edges"
}