# On Mixed Linear Layouts of Series-Parallel Graphs

@inproceedings{Angelini2020OnML, title={On Mixed Linear Layouts of Series-Parallel Graphs}, author={Patrizio Angelini and Michael A. Bekos and Philipp Kindermann and Tamara Mchedlidze}, booktitle={International Symposium Graph Drawing and Network Visualization}, year={2020} }

A mixed s-stack q-queue layout of a graph consists of a linear order of its vertices and of a partition of its edges into s stacks and q queues, such that no two edges in the same stack cross and no two edges in the same queue nest. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed 1-stack 1-queue layout. Recently, Pupyrev disproved this conjectured by demonstrating a planar partial 3-tree that does not admit a 1-stack 1-queue layout. In this note, we strengthen…

## 3 Citations

### Directed Acyclic Outerplanar Graphs Have Constant Stack Number

- MathematicsArXiv
- 2022

The stack number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k -coloring of the edges such that no two edges of the same color cross, i.e.,…

### Parameterized Algorithms for Queue Layouts

- Mathematics, Computer ScienceGD
- 2020

This paper presents two fixed-parameter tractable algorithms that exploit structural properties of graphs to compute optimal queue layouts and uses a more restrictive parameter, the vertex cover number, to solve the problem for arbitrary graphs.

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