Article in volume
Authors:
Title:
$\ell$-covering $k$-hypergraphs are quasi-eulerian
PDFSource:
Discussiones Mathematicae Graph Theory 43(4) (2023) 1091-1102
Received: 2021-01-07 , Revised: 2021-06-28 , Accepted: 2021-06-28 , Available online: 2021-07-19 , https://doi.org/10.7151/dmgt.2422
Abstract:
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 $\ell$-covering
$k$-hypergraph, for $2 \le \ell < k$, is a $k$-uniform hypergraph in which
every $\ell$-subset of vertices lie together in at least one edge.
In this paper we prove that every $\ell$-covering $k$-hypergraph, for $k \ge 3$,
admits an Euler family.
Keywords:
$\ell$-covering $k$-hypergraph, Euler family, Euler tour, Lovász's $(g,f)$-factor theorem
References:
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https://doi.org/10.37236/416 - L. Lovász, The factorization of graphs II, Acta Math. Acad. Sci. Hungar. 23 (1972) 223–246.
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arXiv: 2101.04561
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