On PVPG graphs: a subclass of vertex intersection graphs of paths on a grid - Alcón, Liliana Graciela (2021)
In this paper, we study the class of PVPG graphs, this is a subclass of VPG graphs such that all the representing paths are between two parallel lines of the grid and have their endpoints on these lines. We prove that PVPG = Co-comparability. Moreover, we present some minimal forbidden induced subgraphs for the class of B1-PVPG graphs.