vix.ing · top · new · best · stats

Cycle decompositions in 3-uniform hypergraphs

2021/01/28 by Simón Piga, Piga, Simón, Nicolás Sanhueza‐Matamala +2
Computer Science · Engineering · Mathematics · #05C45 #05C65 #05C70 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #msc:05C45 #msc:05C65 #msc:05C70

paper · pdf · doi:10.48550/arxiv.2101.12205

28 pages, fixed small errors in references and compilation

openalex publication_date 2021/01/28 · arxiv created 2021/01/31 · arxiv updated 2021/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that 3-graphs on n vertices whose 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 the o(1) term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn, and Osthus.

Related