# Efficient Testing of Large Graphs

@article{Alon1999EfficientTO, title={Efficient Testing of Large Graphs}, author={Noga Alon and Eldar Fischer and Michael Krivelevich and Mario Szegedy}, journal={Combinatorica}, year={1999}, volume={20}, pages={451-476} }

P be a property of graphs. An -test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it has to be modified by adding and removing more than edges to make it satisfy P. The property P is called testable, if for every there exists an -test for P whose total number of queries is independent of…

## 349 Citations

### Testing graphs for colorability properties *

- MathematicsRandom Struct. Algorithms
- 2005

It is proven here that other classes of graph properties, describable by various generalizations of the coloring notion used in Alon et al. are testable, showing that this approach can broaden the understanding of the nature of the testable graph properties.

### A combinatorial characterization of the testable graph properties: it's all about regularity

- Mathematics, Computer ScienceSTOC '06
- 2006

One of the main open problems in the area of property-testing, which was raised in the 1996 paper of Goldreich, Goldwasser and Ron, is resolved by a purely combinatorial characterization of the graph properties that are testable with a constant number of queries.

### Testing Property of graphs: Introduction and a few examples

- Mathematics
- 2008

A property tester determines whether a graph G = (V,E) has a given property or is far from having the property (‘far’ from having a property will be defined later on depending on the graph…

### A Characterization of Graph Properties Testable for General Planar Graphs with one-Sided Error (It's all About Forbidden Subgraphs)

- Mathematics, Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

The sufficient condition in the characterization reduces the problem to the task of testing H-freeness in planar graphs, and is the main and most challenging technical contribution of the paper.

### A characterization of testable hypergraph properties [ Extended Abstract ]

- Mathematics
- 2017

We provide a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs). Here, a k-graph property P is testable if there is a randomized algorithm which makes…

### Testing Hereditary Properties of Nonexpanding Bounded-Degree Graphs

- Mathematics, Computer ScienceSIAM J. Comput.
- 2007

It is shown that every hereditary graph property is testable with a constant number of queries provided that every sufficiently large induced subgraph of the input graph has poor expansion.

### Testing Hereditary Properties of Ordered Graphs and Matrices

- Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

The proof bridges the gap between techniques related to the regularity lemma, used in the long chain of papers investigating graph testing, and string testing techniques and develops a Ramsey-type lemma for multipartite graphs with undesirable edges.

### Efficient Testing of Hypergraphs

- MathematicsICALP
- 2002

It is proved that if more than ?n3 (? > 0) triples must be added or deleted from a 3-graph H on n vertices to destroy all induced copies of F, then H must contain ? cn |V(F)| induced copiesof F, as long as n ? n0(?,F).

### Testing graphs against an unknown distribution

- MathematicsElectron. Colloquium Comput. Complex.
- 2019

This paper completely solve Goldreich’s problem by giving a precise characterization of the graph properties that are testable in the Vertex-Distribution-Free model.

### A Characterization of Testable Hypergraph Properties

- Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

This work provides a combinatorial characterization of all testable properties of k-graphs (i.e. k-uniform hypergraphs) and shows 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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