On Layered Fan-Planar Graph Drawings
Computational Geometry
2020-02-25 v1 Discrete Mathematics
Abstract
In this paper, we study fan-planar drawings that use layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in , via a reduction to a similar result for planar graphs by Dujmovi\'{c} et al. If the embedding is not fixed, then we give partial results for : It was already known how to test existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper -layer drawings; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.
Cite
@article{arxiv.2002.09597,
title = {On Layered Fan-Planar Graph Drawings},
author = {Therese Biedl and Steven Chaplick and Jiři Fiala and Michael Kaufmann and Fabrizio Montecchiani and Martin Nöllenburg and Chrysanthi Raftopoulou},
journal= {arXiv preprint arXiv:2002.09597},
year = {2020}
}