文章基本信息

标题：Layered Fan-Planar Graph Drawings
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作者：Therese Biedl ; Steven Chaplick ; Michael Kaufmann 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：170
页码：14:1-14:13
DOI：10.4230/LIPIcs.MFCS.2020.14
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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 DujmoviÄ 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.
关键词：Graph Drawing; Parameterized Complexity; Beyond Planar Graphs