Packing trees into 1-planar graphs
Affiliation
Department of Computer Science, University of ArizonaIssue Date
2021Metadata
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Brown UniversityCitation
De Luca, F., Di Giacomo, E., Hong, S.-H., Kobourov, S., Lenhart, W., Liotta, G., Meijer, H., Tappini, A., & Wismath, S. (2021). Packing trees into 1-planar graphs. Journal of Graph Algorithms and Applications.Rights
Copyright © The Author(s) 2021. This work is licensed under the terms of the CC-BY license.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We introduce and study the 1-planar packing problem: Given k graphs with n vertices G1, …, Gk, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each Gi is a tree and k = 3. We prove that a triple consisting of three caterpillars or of two caterpillars and a path may not admit a 1-planar packing, while two paths and a special type of caterpillar always have one. We then study 1-planar packings with few crossings and prove that three paths (resp. cycles) admit a 1-planar packing with at most seven (resp. fourteen) crossings. We finally show that a quadruple consisting of three paths and a perfect matching with n ≥ 12 vertices admits a 1-planar packing, while such a packing does not exist if n ≤ 10. © 2021, Brown University. All rights reserved.Note
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1526-1719Version
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Except where otherwise noted, this item's license is described as Copyright © The Author(s) 2021. This work is licensed under the terms of the CC-BY license.