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### Three theorems regarding testing graph properties

O. Goldreich, L. Trevisan
Proceedings 2001 IEEE International Conference on Cluster Computing
We presents three theorems regarding testing graph properties in the adjacency matrix representation.  ...  The second theorem is that every graph property that can be tested making a number of queries that is independent of the size of the graph can be so tested by uniformly selecting a set of vertices and  ...  THREE THEOREMS REGARDING TESTING GRAPH PROPERTIES The closure operation makes this collection correspond to a graph property (since it is now preserved under isomorphism).  ...

### Xor-Magic Graphs

Jacob A. Siehler
2019 Recreational Mathematics Magazine
We classify the 3-regular xor-magic graphs on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic graphs on 32 vertices, including the well-known Dyck graph.  ...  We show that there is at least one 3-regular xor-magic graph on 2n vertices for every n ⩾ 2.  ...  Theorem 2. If G is xor-magic, then (Test 1) k n, and (Test 2) The rows of Y are all distinct. Test 2 is particularly powerful because it applies to any basis for the nullspace. Proof.  ...

### Hierarchy Theorems for Property Testing [chapter]

Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg
2010 Lecture Notes in Computer Science
Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree  ...  That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q).  ...  Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy theorems for the adjacency matrix model.  ...

### Hierarchy Theorems for Property Testing [chapter]

Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg
2009 Lecture Notes in Computer Science
Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree  ...  That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q).  ...  Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy theorems for the adjacency matrix model.  ...

### Hierarchy Theorems for Property Testing

Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg
2011 Computational Complexity
Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree  ...  That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q).  ...  Acknowledgments We are grateful to Ronitt Rubinfeld for asking about the existence of hierarchy theorems the adjacency matrix model.  ...

### Page 7272 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews
Wing-Kin Sung (SGP-SING-CSC; Singapore) 2004i:68081 68Q25 05C85 68Q17 68R10 68W20 68W25 Goldreich, Oded (IL-WEIZ-AC; Rehovot) ; Trevisan, Luca (1-CA-CDE; Berkeley, CA) Three theorems regarding testing  ...  The authors offer improvements of three existing theorems con- cerning testing in the above setting.  ...

### Page 2335 of Mathematical Reviews Vol. , Issue 82f [page]

1982 Mathematical Reviews
With regard to planar graphs it is conjectured that every such graph is 5-choosable and that 5 is best possible.  ...  (Here 9,,,,, is the graph determined by three paths, two of length 2 and one of length 2m, having only end vertices in common.)  ...

### Learning from Few Positives: a Provably Accurate Metric Learning Algorithm to Deal with Imbalanced Data

Rémi Viola, Rémi Emonet, Amaury Habrard, Guillaume Metzler, Marc Sebban
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
Unlike the state-of-the-art methods, our algorithm MLFP, for Metric Learning from Few Positives, learns a new representation that is used only when a test query is compared to a minority training example  ...  property testing.  ...  Graph Property Testing We now investigate the ability of CLIP to identify structural graph properties, a task which was previously used to evaluate the expressivity of graph kernels and on which the Weisfeiler-Lehman  ...

### Avoidable paths in graphs [article]

Marthe Bonamy and Oscar Defrain and Meike Hatzel and Jocelyn Thiebaut
2019 arXiv   pre-print
We provide a constructive and elementary proof, relying on a single trick regarding the induction hypothesis.  ...  Avoidability generalises the notion of simpliciality best known in the context of chordal graphs.  ...  We are indebted to Michał Pilipczuk for providing helpful references regarding the complexity of finding an induced path of given length.  ...

### Avoidable Paths in Graphs

Marthe Bonamy, Oscar Defrain, Meike Hatzel, Jocelyn Thiebaut
2020 Electronic Journal of Combinatorics
We provide a constructive and elementary proof, relying on a single trick regarding the induction hypothesis.  ...  Avoidability generalises the notion of simpliciality best known in the context of chordal graphs.  ...  We are indebted to Micha l Pilipczuk for providing helpful references regarding the complexity of finding an induced path of given length.  ...

### Relating counterexamples to test cases in CTL model checking specifications

Duminda Wijesekera, Paul Ammann, Lingya Sun, Gordon Fraser
2007 Proceedings of the 3rd international workshop on Advances in model-based testing - A-MOST '07
For example, it might take more than one test case to "cover" a given counterexample, because not all property violations can be illustrated with linear counterexamples.  ...  This result can not only be used in the generation of a test set that satisfies a given test coverage criterion, but also in the determination of whether an extant test set satisfies the criterion.  ...  Figure 4 : 4 Three different possible evidence graphs for MC/DC with regard to x in C = x ∧ (y ∨ z). Figure 5 : 5 An AX dangerous evidence graph for property P .  ...

### Sublinear Computation Paradigm: Constant-Time Algorithms and Sublinear Progressive Algorithms

Kyohei CHIBA, Hiro ITO
2021 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
We present Sublinear Progressive Algorithm Theory (SPA Theory, for short), which enables to make a sublinear progressive algorithm for any property if it has a constant-time algorithm and an exact algorithm  ...  Theorem 23 (SPA Theorem: property testing version): Let P be a property.  ...  Note that in O( * ) and Θ( * ) in this theorem, ϵ, r, and t are regarded as variables.  ...

### The Subgraph Testing Model

Oded Goldreich, Dana Ron, Michael Wagner
2018 Innovations in Theoretical Computer Science
We focus on bounded-degree base graphs and on the relation between testing graph properties in the subgraph model and testing the same properties in the bounded-degree graph model.  ...  We initiate a study of testing properties of graphs that are presented as subgraphs of a fixed (or an explicitly given) graph.  ...  Still, let us make a couple of comments regarding cases in which the subgraph testing model coincides with other testing models. The dense graph model is a special case of subgraph testing.  ...

### Every minor-closed property of sparse graphs is testable

Itai Benjamini, Oded Schramm, Asaf Shapira
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
In sharp contrast to property testing of dense graphs, which is relatively well understood, very few properties are known to be testable in bounded degree graphs with a constant number of queries.  ...  In this paper we identify for the first time a large (and natural) family of properties that can be efficiently tested in bounded degree graphs, by showing that every minor-closed graph property can be  ...  In fact, this closure property under these three basic operations holds for the property of a graph being embeddable in any specific surface.  ...

### Every minor-closed property of sparse graphs is testable

Itai Benjamini, Oded Schramm, Asaf Shapira