{
  "abstract": "The linear arrangement of a simple graph $G = (V,E)$ is a bijective labeling $π$ of the vertices of $G$ to the set $\\{1, \\ldots, n\\}$. The maximum linear arrangement ($\\texttt{maxLA}$) problem is to determine whether $G$ has a labeling such that the sum of labels across $G$'s edges, $\\sum_{uv \\in E} |π(u) - π(v)|$, is at least a given value $k$. Minimum linear arrangement ($\\texttt{minLA}$) is defined analogously. Both $\\texttt{maxLA}$ and $\\texttt{minLA}$ are known to be NP complete for general graphs. $\\texttt{minLA}$ has shown to be NP complete for bipartite graphs by Evans and Shiloah in 1975. It has been an open problem whether the same holds for $\\texttt{maxLA}$. In this paper we prove that $\\texttt{maxLA}$ is NP complete for bipartite graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12613",
  "author_total": 2,
  "authors": [
    {
      "name": "Aparna Das"
    },
    {
      "name": "Jonathan Needleman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41r2eyf9p9ar3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12613",
  "fulltext_url": null,
  "id": "41r2eyf9p9ar3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12613",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7221540090",
  "pdf_url": "https://arxiv.org/pdf/2610.12613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41r2eyf9p9ar3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Maximal Linear Arrangement is NP complete on Bipartite Graphs",
  "title_text": "Maximal Linear Arrangement is NP complete on Bipartite Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/41r2eyf9p9ar3",
  "venue": "arXiv",
  "versions": []
}