On Mixed Linear Layouts of Series-Parallel Graphs
Discrete Mathematics
2020-08-26 v2
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.
Keywords
Cite
@article{arxiv.2008.10475,
title = {On Mixed Linear Layouts of Series-Parallel Graphs},
author = {Patrizio Angelini and Michael A. Bekos and Philipp Kindermann and Tamara Mchedlidze},
journal= {arXiv preprint arXiv:2008.10475},
year = {2020}
}
Comments
Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020)