Triple Systems are Eulerian |
| |
| Authors: | Mateja ?ajna Andrew Wagner |
| |
| Institution: | 1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, CanadaEmail: . Phone: +613‐562‐5800 ext. 3522. Mailing address: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada.;2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada |
| |
| Abstract: | An Euler tour of 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, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour. |
| |
| Keywords: | triple system eulerian hypergraph Euler tour 1‐overlap cycle rank‐2 universal cycle Euler family |
|
|
