A unit disk intersection representation (UDR) of a graph $G$ represents each vertex of $G$ as a unit disk in the plane, such that two disks intersect if and only if their vertices are adjacent in $G$. A UDR with interior-disjoint disks is called a unit disk contact representation (UDC). We prove that it is NP-hard to decide if an outerplanar graph or an embedded tree admits a UDR. We further provide a linear-time decidable characterization of caterpillar graphs that admit a UDR. Finally we show that it can be decided in linear time if a lobster graph admits a weak UDC, which permits intersections between disks of non-adjacent vertices.

翻译：圆盘交叉路口表示器(UDR) 代表一张图中每张G$的顶点(UDR) $G$代表飞机中每张G$的单盘盘磁盘,因此,只有两张磁盘的顶点相邻于$G$,而且只有两张磁盘的顶点相互交叉。 带有内分解磁盘的UDR被称为单位磁盘代表器(UDC) 。 我们证明,决定一个外相图或嵌入的树是否接纳UDR是NP硬的。 我们还对接纳UDR的毛虫图作了线性时间分解的线性描述。 最后,我们证明,如果龙虾图接纳了一个弱的UDC,允许非相邻的顶点磁盘交叉,那么它就可以在线性时间里决定。