单位矩形可见性图
Unit Rectangle Visibility Graphs
摘要：
在过去的二十年里，矩形可见性图产生了相当大的兴趣，部分原因是它们适用于超大规模集成电路芯片设计。在这里，我们研究单位矩形可见性图，固定尺寸的限制更紧密地建模在计算机芯片应用中的门和其他电路元件的约束尺寸。一个图$G$是一个单位矩形可见性图（URVG），如果它的顶点可以用平面中的闭单位正方形表示，其边平行于轴，内部两不相交，使得两个顶点相邻当且仅当有一个非退化的水平或垂直可见性带连接两个矩形。我们的结果包括$K_n$，$K_{m,n}$，树是URVG的充要条件，以及一些一般的边缘边界。
英文摘要：
Over the past twenty years, rectangle visibility graphs have generated considerable interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph $G$ is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate horizontal or vertical band of visibility joining the two rectangles. Our results include necessary and sufficient conditions for $K_n$, $K_{m,n}$, and trees to be URVGs, as well as a number of general edge bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
