# Testing Hereditary Properties of Ordered Graphs and Matrices

@article{Alon2017TestingHP, title={Testing Hereditary Properties of Ordered Graphs and Matrices}, author={Noga Alon and Omri Ben-Eliezer and Eldar Fischer}, journal={2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2017}, pages={848-858} }

We consider properties of edge-colored vertex-ordered graphs} – graphs with a totally ordered vertex set and a finite set of possible edge colors – showing that any hereditary property of such graphs is strongly testable, i.e., testable with a constant number of queries. We also explain how the proof can be adapted to show that any hereditary property of two-dimensional matrices over a finite alphabet (where row and column order is not ignored) is strongly testable. The first…

## 16 Citations

### Limits of Ordered Graphs and their Applications.

- Mathematics, Computer Science
- 2018

The theory of graph limits is extended to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which is called an orderon, and it is shown that the space of orderons is compact with respect to this distance notion,Which is key to a successful analysis of combinatorial objects through their limits.

### Polynomial removal lemmas for ordered graphs

- MathematicsCombinatorial Theory
- 2022

. A recent result of Alon, Ben-Eliezer and Fischer establishes an induced removal lemma for ordered graphs. That is, if F is an ordered graph and ε > 0 , then there exists δ F ( ε ) > 0 such that…

### Efficient Removal Lemmas for Matrices Noga Alon

- Mathematics
- 2017

The authors and Fischer recently proved that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a constant…

### Limits of Ordered Graphs and Images

- MathematicsArXiv
- 2018

The theory of graph limits is extended to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which is called an orderon, and it is shown that the space of orderons is compact with respect to this distance notion,Which is key to a successful analysis of combinatorial objects through their limits.

### Ordered Graph Limits and Their Applications

- Mathematics, Computer ScienceITCS
- 2021

An ordered analogue of the well-known result by Alon and Stav on the furthest graph from a hereditary property is proved, the first known result of this type in the ordered setting, and an alternative analytic proof of the ordered graph removal lemma is described.

### Earthmover Resilience and Testing in Ordered Structures

- Mathematics, Computer ScienceElectron. Colloquium Comput. Complex.
- 2018

A wide class of properties of ordered structures - the earthmover resilient (ER) properties - are identified and it is shown that the "good behavior" of such properties allows us to obtain general testability results that are similar to (and more general than) those of unordered graphs.

### C O ] 1 7 Ju l 2 01 9 Ordered Graph Limits and Their Applications

- Mathematics
- 2019

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally…

### Testing Hereditary Properties of Sequences

- MathematicsAPPROX-RANDOM
- 2017

It is shown that there exist hereditary properties of sequences that cannot be tested with sublinear queries, resolving an open question posed by Newman et al.

### Efficient Removal Lemmas for Matrices

- Mathematics, Computer ScienceAPPROX-RANDOM
- 2017

This work establishes much more efficient removal lemmas for several special cases of the above problem and combines their efficient conditional regularity lemma for matrices with additional combinatorial and probabilistic ideas.

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