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arXiv · 2008.10475

On Mixed Linear Layouts of Series-Parallel Graphs

Patrizio Angelini·Michael A. Bekos·Philipp Kindermann·Tamara Mchedlidze
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Abstract

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 Pupyrev's result by showing that the conjecture does not hold even for 2-trees, also known as series-parallel graphs.

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Patrizio Angelini, Michael A. Bekos, Philipp Kindermann, Tamara Mchedlidze. 2020-08-24. On Mixed Linear Layouts of Series-Parallel Graphs. https://arxiv.org/abs/2008.10475

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