2021/01/12 by Mateja Šajna, Andrew Wagner, Šajna, Mateja +1 · 1 citation
Mathematics · #05C45 #05C65 #05C70 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C45 #msc:05C65 #msc:05C70
paper · pdf · doi:10.48550/arxiv.2101.04561
arxiv created 2021/01/12 · arxiv updated 2021/01/13
An Euler tour in a hypergraph (also called a rank-2 universal cycle or 1-overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, we define a covering k-hypergraph to be a non-empty k-uniform hypergraph in which every (k-1)-subset of vertices appear together in at least one edge. We then show that every covering k-hypergraph, for k≥ 3, admits an Euler tour if and only if it has at least two edges.