A characterization of testable hypergraph properties
We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that sa...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
6 May 2025
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| In: |
Journal of combinatorial theory
Year: 2025, Volume: 174, Pages: 133-189 |
| DOI: | 10.1016/j.jctb.2025.04.009 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.jctb.2025.04.009 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0095895625000292 
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| Author Notes: | Felix Joos, Jaehoon Kim, Daniela Kühn, Deryk Osthus |
| Summary: | We provide a combinatorial characterization of all testable properties of k-uniform hypergraphs (k-graphs for short). Here, a k-graph property P is testable if there is a randomized algorithm which makes a bounded number of edge queries and distinguishes with probability 2/3 between k-graphs that satisfy P and those that are far from satisfying P. For the 2-graph case, such a combinatorial characterization was obtained by Alon, Fischer, Newman and Shapira. Our results for the k-graph setting are in contrast to those of Austin and Tao, who showed that for the somewhat stronger concept of local repairability, the testability results for graphs do not extend to the 3-graph setting. |
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| Item Description: | Gesehen am 28.10.2025 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.jctb.2025.04.009 |