{
  "abstract": "The Eccentricity Shortest Path problem asks, given a connected graph and a nonnegative integer $R$, whether some shortest path is within distance $R$ of every vertex. We study its structural parameterized complexity. We give fixed-parameter algorithms for vertex-deletion distance to cographs, vertex-deletion distance to interval graphs, and bandwidth. The interval-deletion result answers a question of Bhyravarapu et al. (IWOCA 2023). We obtain XP algorithms for vertex-deletion distance to chordal graphs, clique-width, and rank-width, without requiring expressions or decompositions for the latter two. Consequently, the problem is polynomial-time solvable for every fixed treewidth, answering a question of Chakraborty et al. (2026). We also derive fixed-parameter tractability for treedepth and XP membership for diameter from earlier algorithms. We prove $\\mathsf{W}[3]$-hardness for cutwidth, and hence pathwidth and treewidth, even on graphs of maximum degree at most five; $\\mathsf{W}[2]$-hardness for vertex clique-cover number; and NP-hardness on graphs of tree-independence number at most two. For maximum leaf number $\\ell$, we obtain an $O(\\ell^4)$-bit compression and a polynomial kernel. Finally, unless $\\mathsf{NP}\\subseteq\\mathrm{coNP}/\\mathrm{poly}$, we exclude polynomial kernels for bandwidth, feedback edge number, vertex-deletion distance to a clique, and vertex cover number. The last bound also excludes polynomial kernels for vertex-deletion distance to proper interval graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20769",
  "author_total": 4,
  "authors": [
    {
      "name": "Anand Babu"
    },
    {
      "name": "Ashwin Jacob"
    },
    {
      "name": "Hitendra Kumar"
    },
    {
      "name": "R. B. Sandeep"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddc933zfk6kkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20769",
  "fulltext_url": null,
  "id": "ddc933zfk6kkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20769",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7222713967",
  "pdf_url": "https://arxiv.org/pdf/2610.20769",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddc933zfk6kkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20769",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20769"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Eccentricity Shortest Path: the structural parameter landscape",
  "title_text": "Eccentricity Shortest Path: the structural parameter landscape",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/ddc933zfk6kkf",
  "venue": "arXiv",
  "versions": []
}