2 problems

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Van der Holst's classification of the obstructions to Colin de Verdière invariant at most 5
Van der Holst's classification conjecture. The graphs in the $K_7$ and $K_{3,3,1,1}$ families are the obstructions to $\mu\leq 5$ .
Conjectureopencolin-de-verdiere-invariant graph-theory knotless-embeddingarXiv posted 2 days ago
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The Colin de Verdière invariant conjecture for graphs on surfaces
Colin de Verdière invariant conjecture. The right bound should be
Conjectureopencolin-de-verdiere-invariant graph-invariants surface-embeddingsarXiv posted 2 days ago

Van der Holst's classification of the obstructions to Colin de Verdière invariant at most 5