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- W4322760710 abstract "A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric arboricity, and hence the geometric thickness, of 2-degenerate graphs is at most 4. On the other hand, we show that there are 2-degenerate graphs that do not admit any straight-line drawing with a decomposition of the edge set into 2 plane graphs. That is, there are 2-degenerate graphs with geometric thickness, and hence geometric arboricity, at least 3. This answers two questions posed by Eppstein [Separating thickness from geometric thickness. In Towards a Theory of Geometric Graphs, vol. 342 of Contemp. Math., AMS, 2004]." @default.
- W4322760710 created "2023-03-03" @default.
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- W4322760710 date "2023-02-28" @default.
- W4322760710 modified "2023-09-30" @default.
- W4322760710 title "On the geometric thickness of 2-degenerate graphs" @default.
- W4322760710 doi "https://doi.org/10.48550/arxiv.2302.14721" @default.
- W4322760710 hasPublicationYear "2023" @default.
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