Abstract
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 language | English (US) |
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Article number | 113504 |
Journal | Discrete Mathematics |
Volume | 346 |
Issue number | 11 |
DOIs | |
State | Accepted/In press - 2023 |
Keywords
- Discharging
- Hypergraphs
- Loose cycles
- Saturation
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics