$\ell$-covering $k$-hypergraphs are quasi-eulerian

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.

arXiv admin note: text overlap with arXiv:2101.04561