Edge Partitions of Complete Geometric Graphs (Part 2)

Edge Partitions of Complete Geometric Graphs (Part 2)

Recently, the second and third author showed that complete geometric graphs on $2n$ vertices in general cannot be partitioned into $n$ plane spanning trees. Building up on this work, in this paper, we initiate the study of partitioning into beyond planar subgraphs, namely into $k$-planar and $k$-qua...

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Hauptverfasser: Aichholzer, Oswin, Obenaus, Johannes, Orthaber, Joachim, Paul, Rosna, Schnider, Patrick, Steiner, Raphael, Taubner, Tim, Vogtenhuber, Birgit
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Computational Geometry
Mathematics - Combinatorics
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Zusammenfassung:Recently, the second and third author showed that complete geometric graphs on $2n$ vertices in general cannot be partitioned into $n$ plane spanning trees. Building up on this work, in this paper, we initiate the study of partitioning into beyond planar subgraphs, namely into $k$-planar and $k$-quasi-planar subgraphs and obtain first bounds on the number of subgraphs required in this setting.
DOI:10.48550/arxiv.2112.08456