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On a problem of Specker about Euclidean ...

Van Thé, L. Nguyen...

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On a problem of Specker about Euclidean representations of finite graphs by Van Thé, L. Nguyen ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-08-2023
Summary	Say that a graph $G$ is \emph{representable in $\R ^n$} if there is a map $f$ from its vertex set into the Euclidean space $\R ^n$ such that $\\| f(x) - f(x')\\| = \\| f(y) - f(y')\\|$ iff $\{x,x'\}$ and $\{y, y'\}$ are both edges or both non-edges in $G$. The purpose of this note is to present the proof of the following result, due to Einhorn and Schoenberg: if $G$ finite is neither complete nor independent, then it is representable in $\R ^{\|G\|-2}$. A similar result also holds in the case of finite complete edge-colored graphs.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/0810.2359

Citation

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AMA 11th EditionReferences

Van Thé, L. Nguyen. On a problem of Specker about Euclidean representations of finite graphs. Australian National University. August 01, 2023. Accessed November 07, 2024. https://online.provdatabase.com/cite/2251

APA 7th EditionReferences

Van Thé, L. Nguyen. (2023). On a problem of Specker about Euclidean representations of finite graphs. Australian National University. https://online.provdatabase.com/cite/2251

Chicago 17th EditionReferences

Van Thé, L. Nguyen. On a problem of Specker about Euclidean representations of finite graphs. Australian National University. 2023. https://online.provdatabase.com/cite/2251

HarvardReferences

Van Thé, L. Nguyen. (2023). On a problem of Specker about Euclidean representations of finite graphs. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/2251. (Accessed 07 November 2024).

Harvard AustraliaReferences

Van Thé, L. Nguyen, 2023, On a problem of Specker about Euclidean representations of finite graphs, Australian National University, viewed 07 November 2024, <https://online.provdatabase.com/cite/2251>

MLA 9th EditionWorks Cited

Van Thé, L. Nguyen. On a problem of Specker about Euclidean representations of finite graphs. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/2251.

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