Characterization and a 2D Visualization of B_0-VPG Cocomparability Graphs

08/05/2020

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by   Sreejith K. Pallathumadam, et al.

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B_0-VPG graphs are intersection graphs of vertical and horizontal line segments on a plane. Cohen, Golumbic, Trotter, and Wang [Order, 2016] pose the question of characterizing B_0-VPG permutation graphs. We respond here by characterizing B_0-VPG cocomparability graphs. This characterization also leads to a polynomial time recognition and B_0-VPG drawing algorithm for the class. Our B_0-VPG drawing algorithm starts by fixing any one of the many posets P whose cocomparability graph is the input graph G. The drawing we obtain not only visualizes G in that one can distinguish comparable pairs from incomparable ones, but one can also identify which among a comparable pair is larger in P from this visualization.