Characterization and a 2D Visualization of B_0-VPG Cocomparability Graphs
share
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.
READ FULL TEXT