Further applications of the rank-lower-bound lemma

Determine whether Lemma 4.02 and the proof techniques based on certifying membership of the vectors can be applied to obtain new rank lower bounds or breakthroughs for other convex relaxation hierarchies.

Background

Lemma 4.02 provides a general mechanism for proving LovszSchrijver -rank lower bounds without constructing explicit numerical certificates. The paper applies this mechanism to stretched cliques by tracking vectors that behave well under vertex deletion and destruction.

The authors deliberately formulate the lemma for general relaxations and identify its possible relevance beyond the stable-set setting. Whether the lemma and its underlying ideas have useful applications elsewhere is left unresolved.