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

On the Deque and Rique Numbers of Complete and Complete Bipartite Graphs