发表机构
School of Mathematics and Statistics, Lanzhou University; School of Mathematics and Statistics, Huaibei Normal University（兰州大学数学与统计学院; 淮北师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了最大度分别为8和11的平面$B_0$-CPG与$B_1$-CPG图的识别问题是NP完全的，解决了该领域两个长期开放的识别难题。
AI 中文摘要
$k$-弯折路径是一条位于网格上、由至多 $k+1$ 条轴平行线段组成的非自交折线。$B_k$-CPG 图是这样一类图：其顶点可以用网格上两两内部不相交的 $k$-弯折路径表示，且两个顶点相邻当且仅当对应的网格路径在某个网格点接触。我们证明了识别最大度为 8 的平面 $B_0$-CPG 图是 NP 完全的，并且识别最大度为 11 的平面 $B_1$-CPG 图也是 NP 完全的。这些结果解决了 Champseix、Galby、Munaro 和 Ries 留下的三个平面识别问题中的两个。
英文摘要
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.
Comments20 pages, 8 figures
