2021/01/27 by Mateja Šajna, Andrew Wagner, Šajna, Mateja +1
Mathematics · #05C45 #05C65 #05C70 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C45 #msc:05C65 #msc:05C70
paper · pdf · doi:10.48550/arxiv.2101.11165
arXiv admin note: text overlap with arXiv:2101.04561
arxiv created 2021/01/27 · arxiv updated 2021/01/28
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 < 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.