1 Correction to: Algorithmica (2016) 74:1293–1320 https://doi.org/10.1007/s00453-015-0002-1
In Theorem 8 of our article “Outer-1-Planar Graphs” (Algorithmica 74(4), pp. 1293–1320, [1]), we erroneously claim that every outer 1-planar graph admits a planar visibility representation in \(\mathcal {O}(n \log n)\) area. This statement has recently been disproved by Biedl (GD 2020, LNCS 12590, pp. 526–528, [2]), who showed that there are outer 1-planar graphs with an area requirement of \(\Omega (n^2)\) in any planar polyline drawing. The other results of our article remain unaffected.
References
Auer, C., Bachmaier, C., Brandenburg, F.J., Gleißner, A., Hanauer, K., Neuwirth, D., Reislhuber, J.: Outer 1-planar graphs. Algorithmica 74(4), 1293–1320 (2016). https://doi.org/10.1007/s00453-015-0002-1
Biedl, T.: Drawing outer-1-planar graphs revisited. In: D. Auber, P. Valtr (eds.) Graph Drawing and Network Visualization—28th International Symposium, GD 2020, Vancouver, BC, Canada, 16–18 Sept 2020, Proceedings, Lecture Notes in Computer Science, vol. 12590, pp. 526–528. Springer (2020). https://doi.org/10.1007/978-3-030-68766-3
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Auer, C., Bachmaier, C., Brandenburg, F.J. et al. Correction to: Outer 1-Planar Graphs. Algorithmica 83, 3534–3535 (2021). https://doi.org/10.1007/s00453-021-00874-z
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DOI: https://doi.org/10.1007/s00453-021-00874-z