Dominating Set on Overlap Graphs of Rectangles Intersecting a Line

A graph \(G = (V, E)\) is called a rectangle overlap graph if there is a bijection between V and a set \(\mathcal {R}\) of axis-parallel rectangles such that two vertices in V are adjacent if and only if the corresponding rectangles in \(\mathcal {R}\) overlap i.e. their boundaries intersect.

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