Characterization and a 2D Visualization of B$_0$-VPG Cocomparability Graphs

DOI10.1007/978-3-030-68766-3_16arXiv2008.02173MaRDI QIDQ6346550

Deepak Rajendraprasad, Sreejith K. Pallathumadam

Publication date: 5 August 2020

Abstract: 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.

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

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