$(K_{5,5}\) is fully reconstructible in $\mathbb{C}^3$$

(K_{5,5}\) is fully reconstructible in $\mathbb{C}^3$

A graph $G$ is fully reconstructible in $\mathbb{C}^d$ if the graph is determined from its $d$-dimensional measurement variety. The full reconstructibility problem has been solved for $d=1$ and $d=2$. For $d=3$, some necessary and some sufficient conditions are known and $K_{5,5}$ fall...

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Veröffentlicht in:	arXiv.org 2022-11
Hauptverfasser:	Daniel Irving Bernstein, Gortler, Steven J
Format:	Artikel
Sprache:	eng
Schlagworte:	Dimensional measurement
Online-Zugang:	Volltext
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Zusammenfassung:	A graph $G$ is fully reconstructible in $\mathbb{C}^d$ if the graph is determined from its $d$-dimensional measurement variety. The full reconstructibility problem has been solved for $d=1$ and $d=2$. For $d=3$, some necessary and some sufficient conditions are known and $K_{5,5}$ falls squarely within the gap in the theory. In this paper, we show that $K_{5,5}$ is fully reconstructible in $\mathbb{C}^3$.
ISSN:	2331-8422

Zusammenfassung:	A graph \(G\) is fully reconstructible in \(\mathbb{C}^d\) if the graph is determined from its \(d\)-dimensional measurement variety. The full reconstructibility problem has been solved for \(d=1\) and \(d=2\). For \(d=3\), some necessary and some sufficient conditions are known and \(K_{5,5}\) falls squarely within the gap in the theory. In this paper, we show that \(K_{5,5}\) is fully reconstructible in \(\mathbb{C}^3\).
ISSN:	2331-8422

(K_{5,5}\) is fully reconstructible in \(\mathbb{C}^3\)