{
  "abstract": "We consider $l$-Euler trails and $l$-Euler circuits in finite $k$-uniform directed multihypergraphs, where $k\\geq 2$ and $1\\leq l<k$. Let $D$ be such a directed multihypergraph. The notions of $l$-connectivity and $l$-balance are defined in terms of the $l$-tails and $l$-heads of its hyperarcs. It is shown that $D$ is $l$-Eulerian if and only if $D$ is $l$-connected and $l$-balanced. Moreover, $D$ is $l$-semi-Eulerian if and only if $D$ is $l$-connected and has exactly two states with unequal $l$-indegrees and $l$-outdegrees, one with $l$-outdegree one greater than its $l$-indegree and the other with $l$-indegree one greater than its $l$-outdegree. The proofs are based on an $l$-transition digraph and the classical Euler theorem for directed multigraphs. The corresponding conditions for $k$-uniform multihypergraphs are also obtained in terms of their orientations. For a given orientation, an expected linear-time algorithm is provided to determine whether an $l$-Euler trail or an $l$-Euler circuit exists and to construct one when it does.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02742",
  "author_total": 3,
  "authors": [
    {
      "name": "Yiming Lei"
    },
    {
      "name": "Chenxi Lv"
    },
    {
      "name": "Bing Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8807eyx4d818g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02742",
  "fulltext_url": null,
  "id": "8807eyx4d818g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02742",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8807eyx4d818g.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "k-uniform l-Eulerian hypergraphs",
  "title_text": "k-uniform l-Eulerian hypergraphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8807eyx4d818g",
  "venue": "arXiv",
  "versions": []
}