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
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.