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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 )
Lemonjar Open Access
N.A
31-07-2023
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.
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English
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MYR 0.01
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http://arxiv.org/abs/0810.2359
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