Bar visibility graphs were introduced in the seventies as a model for some VLSI layout problems. They have been also studied since then by the graph drawing community, and recently several generalizations and restricted versions have been proposed. We introduce a generalization, witness-bar visibility graphs, and we prove that this class encom- passes all the bar-visibility variations considered so far. In addition, we show that many classes of graphs are contained in this family, including in particular all planar graphs, interval graphs, circular arc graphs and permutation graphs

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