Several types of linear layouts of graphs are obtained by leveraging known data structures; the most notable representatives are the stack and the queue layouts. In this content, given a data structure, one seeks to specify an order of the vertices of the graph and a partition of its edges into pages, such that the endpoints of the edges assigned to each page can be processed by the given data structure in the underlying order. In this paper, we study deque and rique layouts of graphs obtained by leveraging the double-ended queue and the restricted-input double-ended queue (or deque and rique, for short), respectively. Hence, they generalize both the stack and the queue layouts. We focus on complete and complete bipartite graphs and present bounds on their deque- and rique-numbers, that is, on the minimum number of pages needed by any of these two types of linear layouts.

翻译：通过利用已知数据结构可以获取图的多种线性布局，其中最典型的代表是栈布局和队列布局。在此背景下，给定一种数据结构，需要确定图的顶点顺序以及边到页面的划分，使得分配给每个页面的边端点能够按照基础顺序由该数据结构处理。本文分别研究了通过利用双端队列和受限输入双端队列（简称双端队列和受限输入队列）获得的图的双端队列布局和受限输入队列布局。因此，这两种布局同时推广了栈布局和队列布局。我们重点关注完全图和完全二部图，并给出了它们的双端队列数和受限输入队列数的界，即这两种线性布局所需的最小页面数。