Given a partial cube \(G\), the \(\Theta\)-graph of \(G\) has \(\Theta\)-classes of \(G\) as its vertices, and two vertices in it are adjacent if the corresponding \(\Theta\)-classes meet in a vertex of \(G\). We present a counter-example to the question from \([8]\) whether \(\Theta\)-graphs of graphs of acyclic cubical complexes are always dually chordal graphs. On a positive side, we show that in the class of ACC \(p\)-expansion graphs, each \(\Theta\)-graph is both a dually chordal and a chordal graph. In the proof, a fundamental characterization of \(\Theta\)-acyclic hypergraphs is combined with techniques from metric graph theory. Along the way, we also introduce a new, weaker version of simplicial elimination scheme, which yields yet another characterization of chordal graphs.
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