CPG graphs: Some structural and hardness results

In this paper we continue the systematic study of Contact graphs Paths on a Grid ( CPG ) initiated in Deniz et al. (2018). A graph is for which there exists collection pairwise interiorly disjoint paths grid one-to-one correspondence with its vertex set such that two vertices are adjacent if and only corresponding touch at grid-point. If every path has most k bends some ? 0 , said to be B -CPG. We first show that, any class -CPG strictly contained + 1 even within planar graphs, thus implying no The main result recognizing NP -complete. Moreover, same remains true case 3 . then consider several problems restricted show, particular, Independent Set Clique Cover remain -hard graphs. Finally, related classes -EPG edge-intersection grid. Although it possible optimally color polynomial time, as coincides interval contrast, 3-Colorability -complete