The mixed page number of graphs

Abstract

A linear layout of a graph typically consists of a total vertex order, and a partition of the edges into sets either of non-crossing edges, called stacks, or of non-nested edges, called queues. The stack (queue) number of a graph is the minimum number of required stacks (queues) in any linear layout of it. 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 layout models.