Covering hypergraphs are Eulerian. Issue 2 (15th March 2022)

• Record Type: Journal Article
• Authors: Šajna, Mateja; Wagner, Andrew
• Is Part Of: Journal of graph theory. Volume 101:Issue 2(2022)
• Page Start: 226
• Page End: 241
• Publication Date: 2022-03-15
• Subjects: 1‐overlap cycle -- covering hypergraph -- Euler family -- Euler tour -- interchanging cycle -- rank‐2 universal cycle; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22821
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: 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 $k$ ‐ hypergraph to be a nonempty k $k$ ‐uniform hypergraph in which every ( k − 1 ) $(k-1)$ ‐subset of vertices appear together in at least one edge. We then show that every covering k $k$ ‐hypergraph, for k ≥ 3 $k\ge 3$, admits an Euler tour if and only if it has at least two edges.