2 problems

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Conjecture that the $(n+1)$ -cube has no dot product representation in $\mathbb R^n$
The no-representation conjecture. The $(n+1)$ -cube has no dot product representation in $\mathbb R^n$ . This conjecture was disproved by the second author, so the claimed nonexisten…
Conjectureopendot-product-graphs graph-representations hypercubesarXiv posted 2 days ago
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Fiduccia et al.'s conjecture on the dot product dimension of graphs
Let $G$ be a graph on $n$ vertices. Its dot product dimension is the least positive integer $d$ for which there is a map $f:V(G)\to\mathbb{R}^d$ such that, for distinct vertices…
Conjectureopendot-product-graphs graph-theoryarXiv posted 2 days ago

Conjecture that the (n+1)(n+1)(n+1)-cube has no dot product representation in Rn\mathbb R^nRn