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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Bibliographic Details
Published in:Journal of combinatorial theory. Series B Vol. 174; pp. 133 - 189
Main Authors: Joos, Felix, Kim, Jaehoon, Kühn, Daniela, Osthus, Deryk
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2025
Subjects:
Hypergraphs
Property testing
Sublinear algorithms
Hypergraphs
Sublinear algorithms
Property testing
ISSN:0095-8956
Online Access:Get full text
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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.
ISSN:0095-8956
DOI:10.1016/j.jctb.2025.04.009