# Limits of Ordered Graphs and Images

@article{BenEliezer2018LimitsOO, title={Limits of Ordered Graphs and Images}, author={Omri Ben-Eliezer and Eldar Fischer and Amit Levi and Yuichi Yoshida}, journal={ArXiv}, year={2018}, volume={abs/1811.02023} }

The emerging theory of graph limits exhibits an interesting analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described naturally in analytic language. We extend the theory of graph limits to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which we call an orderon. Images are an example of dense ordered bipartite graphs, where the rows and the columns constitute the vertices, and pixel…

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## References

SHOWING 1-10 OF 37 REFERENCES

### 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.

### Large Networks and Graph Limits

- Mathematics

The book Large Networks and Graph Limits, xiv + 475 pp., published in late 2012, comprises five parts, the first an illuminating introduction and the last a tantalizing taste of how the scope of the…

### Graph limits and parameter testing

- MathematicsSTOC '06
- 2006

We define a distance of two graphs that reflects the closeness of both local and global properties. We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if…

### Hypergraph limits: A regularity approach

- MathematicsRandom Struct. Algorithms
- 2015

A new proof and construction of hypergraph limits is given, inspired by the original approach of Lovasz and Szegedy, with the key ingredient being a weak Frieze-Kannan type regularity lemma.

### Convergent sequences of sparse graphs: A large deviations approach

- Mathematics, Computer ScienceRandom Struct. Algorithms
- 2017

This paper introduces a new notion of convergence of sparse graphs, which it is called Large Deviations or LD‐convergence, and which is based on the theory of large deviations, and establishes several previously unknown relationships between the other notions of convergence.

### Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing

- Mathematics
- 2007

### Moments of Two-Variable Functions and the Uniqueness of Graph Limits

- Mathematics
- 2008

AbstractFor a symmetric bounded measurable function W on [0, 1]2 and a simple graph F, the homomorphism density
$$t(F,W) = \int _{[0,1]^{V (F)}} \prod_ {i j\in E(F)} W(x_i, x_j)dx .$$ can be thought…

### 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.