Forbidden Patterns in Mixed Linear Layouts
Deborah Haun, Laura Merker, Sergey Pupyrev

TL;DR
This paper introduces thick patterns as a new way to characterize mixed linear layouts in ordered graphs, providing a boundedness criterion for graphs with bounded degree and exploring the limits of finite forbidden pattern characterizations.
Contribution
It presents the concept of thick patterns to characterize bounded mixed page numbers in bounded-degree graphs and shows the impossibility of finite forbidden pattern characterizations for fixed mixed page numbers.
Findings
Bounded maximum degree graphs have bounded mixed page number iff largest thick pattern size is bounded.
No finite forbidden pattern characterization exists for fixed mixed page number $k \,\geq\, 2$.
Introduces thick patterns as a new characterization tool for mixed linear layouts.
Abstract
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue) number of an ordered graph is the minimum number of required stacks (queues). Mixed linear layouts combine these layouts by allowing each set of edges to form either a stack or a queue. The minimum number of stacks plus queues is called the mixed page number. It is well known that ordered graphs with small stack number are characterized, up to a function, by the absence of large twists (that is, pairwise crossing edges). Similarly, ordered graphs with small queue number are characterized by the absence of large rainbows (that is, pairwise nesting edges). However, no such characterization via forbidden patterns is known for mixed linear layouts. We…
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Taxonomy
TopicsArchitecture and Computational Design · Advanced Manufacturing and Logistics Optimization
