2026-08-16T16:43:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12683 2024-03-06T10:50:34Z ddc:004 open_access

Layered Fan-Planar Graph Drawings Biedl, Therese Chaplick, Steven Kaufmann, Michael Montecchiani, Fabrizio Nöllenburg, Martin Raftopoulou, Chrysanthi Graph Drawing Parameterized Complexity Beyond Planar Graphs In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) 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 h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the 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 h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Therese Biedl and Steven Chaplick and Michael Kaufmann and Fabrizio Montecchiani and Martin Nöllenburg and Chrysanthi Raftopoulou 2020 Is Part Of LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2020.14 urn:nbn:de:0030-drops-126835 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.14 eng https://creativecommons.org/licenses/by/3.0/legalcode