The Mixed Page Number of Graphs

TL;DR

This paper introduces the concept of mixed page number in graphs, combining stacks and queues in linear layouts, and explores its properties, bounds, and advantages over traditional layouts.

Contribution

It initiates the study of mixed page number, providing bounds for complete and bipartite graphs and analyzing the edge density of graphs with bounded mixed page number.

Findings

Mixed layouts are more powerful than traditional stacks or queues.

Bounds established for complete and bipartite graphs.

Edge density of graphs with bounded mixed page number analyzed.

Abstract

A linear layout of a graph typically consists of a total vertex order, and a partition of the edges into sets of either non-crossing edges, called stacks, or non-nested edges, called queues. The stack (queue) number of a graph is the minimum number of required stacks (queues) in a linear layout. Mixed linear layouts combine these layouts by allowing each set of edges to form either a stack or a queue. In this work we initiate the study of the mixed page number of a graph which corresponds to the minimum number of such sets. First, we study the edge density of graphs with bounded mixed page number. Then, we focus on complete and complete bipartite graphs, for which we derive lower and upper bounds on their mixed page number. Our findings indicate that combining stacks and queues is more powerful in various ways compared to the two traditional layouts.