# Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal

## Abstract

The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.

- Authors:

- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22094054

- Resource Type:
- Journal Article

- Journal Name:
- Sbornik. Mathematics

- Additional Journal Information:
- Journal Volume: 203; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; BIBLIOGRAPHIES; EUCLIDEAN SPACE; GRAPH THEORY; MATHEMATICAL MODELS

### Citation Formats

```
Oblakov, Konstantin I, and Oblakova, Tat'yana A.
```*Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal*. United States: N. p., 2012.
Web. doi:10.1070/SM2012V203N10ABEH004273.

```
Oblakov, Konstantin I, & Oblakova, Tat'yana A.
```*Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal*. United States. doi:10.1070/SM2012V203N10ABEH004273.

```
Oblakov, Konstantin I, and Oblakova, Tat'yana A. Wed .
"Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal". United States. doi:10.1070/SM2012V203N10ABEH004273.
```

```
@article{osti_22094054,
```

title = {Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal},

author = {Oblakov, Konstantin I and Oblakova, Tat'yana A},

abstractNote = {The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.},

doi = {10.1070/SM2012V203N10ABEH004273},

journal = {Sbornik. Mathematics},

issn = {1064-5616},

number = 10,

volume = 203,

place = {United States},

year = {2012},

month = {10}

}

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