Year: 2026
Type: preprint
Abstract: A $k$-bend path is a non-self-intersecting polyline that lies on a grid and consists of at most $k+1$ axis-parallel line segments. A $B_k$-CPG graph is a graph whose vertices can be represented by pairwise interiorly disjoint $k$-bend paths on a grid such that two vertices are adjacent if and only if the corresponding grid paths touch at a grid point. We prove that recognizing planar $B_0$-CPG graphs of maximum degree 8 is NP-complete, and that recognizing planar $B_1$-CPG graphs of maximum degree 11 is NP-complete. These results settle two of the three planar recognition problems left open by Champseix, Galby, Munaro, and Ries.
Source: arXiv (Cornell University)
Authors: Sun, Bin, Xu, Shou-Jun, Yang, Yu
Institutions: Lanzhou University, Huaibei Normal University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220709215