Cycle Decompositions in 3-Uniform Hypergraphs

Abstrakt

We show that 3-graphs on n vertices whose minimum codegree is at least (2/3+o(1))n can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to a o(1) term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn, and Osthus.