# Queue Layouts of Planar 3-Trees

A queue layout of a graph G consists of a linear order of the vertices of G and a partition of the edges of G into queues, so that no two independent edges of the same queue are nested. The queue number of G is the minimum number of queues required by any queue layout of G. In this paper, we continue the study of the queue number of planar 3-trees. As opposed to general planar graphs, whose queue number is not known to be bounded by a constant, the queue number of planar 3-trees has been shown to be at most seven. In this work, we improve the upper bound to five. We also show that there exist planar 3-trees, whose queue number is at least four; this is the first example of a planar graph with queue number greater than three.

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research
06/15/2021

### On the Queue Number of Planar Graphs

A k-queue layout is a special type of a linear layout, in which the line...
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11/02/2018

### Planar Graphs of Bounded Degree have Constant Queue Number

A queue layout of a graph consists of a linear order of its vertices and...
research
08/19/2020

### Parameterized Algorithms for Queue Layouts

An h-queue layout of a graph G consists of a linear order of its vertice...
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08/12/2020

### The Local Queue Number of Graphs with Bounded Treewidth

A queue layout of a graph G consists of a vertex ordering of G and a par...
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08/24/2020

### On Mixed Linear Layouts of Series-Parallel Graphs

A mixed s-stack q-queue layout of a graph consists of a linear order of ...
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08/07/2017

### Layouts for Plane Graphs on Constant Number of Tracks

A k-track layout of a graph consists of a vertex k colouring, and a tota...
research
09/01/2022

### The Rique-Number of Graphs

We continue the study of linear layouts of graphs in relation to known d...