AI 中文总结
研究外平面图队列数为1的识别问题，证明判定一般外平面图队列数为1是NP难的，而判定极大外平面图队列数为1可在线性时间内完成，还研究了队列数为1的外路径与最大顶点度的相互作用。
AI 中文摘要
图的线性布局定义为顶点的全序和边到页面的划分。在栈（队列）布局中，同一页面上的两条边不能交叉（嵌套）。图的栈（队列）数是栈（队列）布局所需的最小页面数。本文专注于刻画和识别栈数和队列数均为1的图。已知栈数为1的图恰好是外平面图。我们证明：（i）判定给定外平面图的队列数是否为1是NP难的；（ii）判定给定极大外平面图的队列数是否为1可在线性时间内完成。此外，我们研究了队列数为1的外路径与其最大顶点度之间的相互作用。
英文摘要
A linear layout of a graph is defined as a total order of the vertices and a partition of the edges to pages. In a stack (queue) layout, no two edges on the same page may cross (nest). The stack (queue) number of a graph is the minimum number of pages required in a stack (queue) layout. This paper focuses on characterizing and recognizing graphs that have both stack number 1 and queue number 1. It is known that the graphs with stack number 1 are exactly the outerplanar graphs. We show that (i) deciding whether a given outerplanar graph has queue number 1 is NP-hard; (ii) deciding whether a given maximal outerplanar graph has queue number 1 can be done in linear time. Moreover, we investigate the interplay between outerpaths with queue number 1 and their maximum vertex degree.
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