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k-uniform l-Eulerian hypergraphs — arXiv:2611.02742

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02742
License (as archived): CC0-1.0
Archived: 2026-11-03T18:50:38.204Z
SHA-256 of the archived text: 470bdce43fb7c4a5389b609287d3b3d622ec5a6a8dceec207df6def11f1d4fd4
Stable URL of this page: https://metraipolis.com/documento/dc_554e70bc82ba

How to cite

k-uniform l-Eulerian hypergraphs — arXiv:2611.02742 — arXiv (en), https://arxiv.org/abs/2611.02742 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_554e70bc82ba (Metraipolis archive dc_554e70bc82ba, sha256 470bdce43fb7c4a5389b609287d3b3d622ec5a6a8dceec207df6def11f1d4fd4)

BibTeX

@misc{dc554e70bc82ba,
  title = {k-uniform l-Eulerian hypergraphs — arXiv:2611.02742},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02742},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_554e70bc82ba; sha256 470bdce43fb7c4a5389b609287d3b3d622ec5a6a8dceec207df6def11f1d4fd4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02742. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.02742 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:38.097Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).