Abstract | ||
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The resolution of a drawing plays a crucial role when defining criteria for its quality and readability. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. We continue the study of the recently introduced stub resolution as an additional aesthetic criterion for nonplanar drawings of graphs. A crossed edge is divided into parts, called stubs, which should not be too short for the sake of readability. Thus, the stub resolution of a drawing is defined as the minimum ratio between the length of a stub and the length of the entire edge containing that stub, over all the edges of the drawing. As a meaningful graph class, where crossings are naturally involved, we consider 1-planar graphs (i.e., graphs that allow planar drawings in which every edge is crossed at most once). In an attempt to prove the conjecture that the stub resolution of 1-planar graphs is bounded, we closely investigate a class of maximal 1-planar graphs arising from double-wheels. We show that each such graph allows a straight-line 1-planar drawing with stub resolution 1/5. |
Year | DOI | Venue |
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2018 | 10.1007/978-3-319-74180-2_18 | ALGORITHMS AND DISCRETE APPLIED MATHEMATICS, CALDAM 2018 |
DocType | Volume | ISSN |
Conference | 10743 | 0302-9743 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
6 |
Name | Order | Citations | PageRank |
---|---|---|---|
Michael Kaufmann | 1 | 1224 | 107.33 |
Jan Kratochvíl | 2 | 1751 | 151.84 |
Fabian Lipp | 3 | 0 | 0.68 |
Fabrizio Montecchiani | 4 | 261 | 37.42 |
Chrysanthi N. Raftopoulou | 5 | 32 | 8.53 |
Pavel Valtr | 6 | 397 | 77.30 |