Saturation for the 3-uniform loose 3-cycle

Sean English, Alexandr Kostochka, Dara Zirlin

Research output: Contribution to journalArticlepeer-review


Let F and H be k-uniform hypergraphs. We say H is F-saturated if H does not contain a subgraph isomorphic to F, but H+e does for any hyperedge e∉E(H). The saturation number of F, denoted satk(n,F), is the minimum number of edges in an F-saturated k-uniform hypergraph H on n vertices. Let C3(3) denote the 3-uniform loose cycle on 3 edges. In this work, we prove that ([Formula presented]+o(1))n≤sat3(n,C3(3))≤[Formula presented]n+O(1). This is the first non-trivial result on the saturation number for a fixed short hypergraph cycle.

Original languageEnglish (US)
Article number113504
JournalDiscrete Mathematics
Issue number11
StatePublished - Nov 2023


  • Discharging
  • Hypergraphs
  • Loose cycles
  • Saturation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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