For cycle-completable graphs the algebraic boundary of the elliptope E(G) is a union of determinantal hypersurfaces and Lissajous varieties, and is disjoint from the interior precisely when G is chordal.
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The Algebraic Boundary of Graph Elliptopes
For cycle-completable graphs the algebraic boundary of the elliptope E(G) is a union of determinantal hypersurfaces and Lissajous varieties, and is disjoint from the interior precisely when G is chordal.