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

TL;DR

This paper investigates the minimum number of pages needed for deque and rique layouts of complete and complete bipartite graphs, generalizing stack and queue layouts, and provides bounds for these parameters.

Contribution

It introduces bounds on deque- and rique-numbers for complete and bipartite graphs, extending known results from stack and queue layouts.

Findings

Bounds established for deque-numbers of complete graphs

Bounds established for rique-numbers of bipartite graphs

Generalization of stack and queue layouts to deque and rique layouts

Abstract

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.