{
  "abstract": "A $k$-bend path is a non-self-intersecting polyline that lies on a grid and consists of at most $k+1$ axis-parallel line segments. An $\\llcorner$-EPG graph is a graph whose vertices can be represented by 1-bend paths on a grid, where each path is either $\\llcorner$, $\\shortmid$, or $\\text{-}$, such that two vertices are adjacent if and only if the corresponding paths share at least one grid edge. Characterizing chordal $\\llcorner$-EPG graphs was explicitly posed as an open problem by Cameron, Chaplick, and Hoàng. We resolve this by giving two equivalent characterizations of connected chordal $\\llcorner$-EPG graphs. The first assigns to every connected chordal $\\llcorner$-EPG graph an ordered clique partition tree of its vertex set, where the underlying tree is the bipartite incidence graph of the horizontal and vertical edge-intersection components. The second is stated purely in terms of maximal cliques: a connected chordal graph is $\\llcorner$-EPG if and only if some clique tree admits an admissible partial orientation. A reduction lemma replaces local clique labels by maximal cliques, linking the two characterizations. For a prescribed clique tree, the existence of an admissible partial orientation reduces to 2-SAT and is decided in $O(nM^2)$ time, where $n$ and $M$ are the numbers of vertices and maximal cliques. Finally, we show that strong chordality is not sufficient: we exhibit a strongly chordal graph that is a minimal forbidden induced subgraph for $\\llcorner$-EPG, and a family of split graphs with a unique clique tree for which membership in $\\llcorner$-EPG reduces to a neighborhood condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09443",
  "author_total": 3,
  "authors": [
    {
      "name": "Bin Sun"
    },
    {
      "name": "Shou-Jun Xu"
    },
    {
      "name": "Yu Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wqdynm8g8qdt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09443",
  "fulltext_url": null,
  "id": "5wqdynm8g8qdt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09443",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7220936037",
  "pdf_url": "https://arxiv.org/pdf/2610.09443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wqdynm8g8qdt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Characterizing chordal $\\llcorner$-EPG graphs via admissible clique tree orientations",
  "title_text": "Characterizing chordal llcorner-EPG graphs via admissible clique tree orientations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/5wqdynm8g8qdt",
  "venue": "arXiv",
  "versions": []
}