Euler tours in hypergraphs

S Glock, F Joos, D Kühn, D Osthus - Combinatorica, 2020 - Springer
… We show that a quasirandom k-uniform hypergraph G has a tight Euler tour subject to the
necessary condition that k divides all vertex degrees. The case when G is complete confirms a …

On tours that contain all edges of a hypergraph

Z Lonc, P Naroski - The electronic journal of combinatorics, 2010 - combinatorics.org
… of an Euler tour in a certain class of 3-uniform hypergraphs containing the … Euler tour in
a certain class of 3-uniform hypergraphs containing the class of strongly connected hypergraphs

Eulerian properties of hypergraphs

MA Bahmanian, M Šajna - arXiv preprint arXiv:1608.01040, 2016 - arxiv.org
hypergraphs with Euler tours and Euler families. First, we examine the necessary conditions
for a hypergraph to admit an Euler tour or Euler … sufficient for general hypergraphs. On the …

Spanning Euler Tours in Hypergraphs

A Bahmanian, S Shan - arXiv preprint arXiv:2403.12713, 2024 - arxiv.org
… All our results on Euler families and spanning Euler tours (and consequently, on Hamiltonicity
of the line graph of the hypergraph under consideration) are constructive and are of …

Tight Euler tours in uniform hypergraphs-computational aspects

Z Lonc, P Naroski, P Rzążewski - Discrete Mathematics & …, 2017 - dmtcs.episciences.org
Euler tour in a 3-uniform hypergraph cannot be decided in time 2o(m) (where m denotes the
number of edges of the input hypergraph)… tight Euler trails and tours in the input hypergraph. …

Eulerian Properties of Design Hypergraphs and Hypergraphs with Small Edge Cuts

A Wagner - arXiv preprint arXiv:1905.06459, 2019 - arxiv.org
… finding an Euler tour in a hypergraph to finding an Euler tour in each of the connected
components of the edge-deleted subhypergraph, then show how these individual Euler tours can …

Using edge cuts to find Euler tours and Euler families in hypergraphs

M Šajna, A Wagner - Discrete Mathematics, 2023 - Elsevier
… each edge of the hypergraph exactly once, while an Euler family is a family … Euler tour (family)
in a hypergraph H can be reduced to the analogous problem in some smaller hypergraphs

Quasi-eulerian hypergraphs

A Bahmanian, M Šajna - The Electronic Journal of Combinatorics, 2017 - combinatorics.org
… existence of an Euler family in an arbitrary hypergraph, and … -uniform hypergraph without
cut edges admits an Euler family… an Euler tour to hypergraphs: we define a flag-traversing tour

[HTML][HTML] Spanning Euler tours and spanning Euler families in hypergraphs with particular vertex cuts

Y Steimle, M Šajna - Discrete Mathematics, 2018 - Elsevier
Euler tour and a spanning Euler family, that is, an Euler tour (family) that also traverses each
vertex of the hypergraph … conditions for a hypergraph to admit a spanning Euler family, most …

Covering hypergraphs are Eulerian

M Šajna, A Wagner - Journal of Graph Theory, 2022 - Wiley Online Library
… k $k$ -hypergraph, for k ≥ 3 $k\ge 3$ , admits an Euler tour if … The covering property of
the hypergraph is used both in the … that our 3-hypergraph admits an Euler family and that its …