Geodesic
$ \mathcal{l} $-covering $k$-hypergraphs are quasi-eulerian
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1091-1102

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An Euler tour in a hypergraph H is a closed walk that traverses each edge of H exactly once and an Euler family is a family of closed walks that jointly traverse each edge of H exactly once. An 𝓁-covering k-hypergraph, for 2 ≤𝓁 lt; k, is a k-uniform hypergraph in which every 𝓁-subset of vertices lie together in at least one edge. In this paper we prove that every 𝓁-covering k-hypergraph, for k ≥ 3, admits an Euler family.
Keywords: l-covering k-hypergraph, Euler family, Euler tour, Lovász's (g,f)-factor theorem 
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Šajna, Mateja; Wagner, Andrew. $ \mathcal{l} $-covering $k$-hypergraphs are quasi-eulerian. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1091-1102. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a11/