Projects per year
Abstract
Károlyi, Pach, and Tóth proved that every 2-edge-colored straight-line drawing of the complete graph contains a monochromatic plane spanning tree. It is open if this statement generalizes to other classes of drawings, specifically, to simple drawings of the complete graph. These are drawings where edges are represented by Jordan arcs, any two of which intersect at most once. We present two partial results towards such a generalization. First, we show that the statement holds for cylindrical simple drawings. (In a cylindrical drawing, all vertices are placed on two concentric circles and no edge crosses either circle.) Second, we introduce a relaxation of the problem in which the graph is k-edge-colored, and the target structure must be hypochromatic, that is, avoid (at least) one color class. In this setting, we show that every ⌈(n+5)/6⌉-edge-colored monotone simple drawing of Kn contains a hypochromatic plane spanning tree. (In a monotone drawing, every edge is represented as an x-monotone curve.)
Original language | English |
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Title of host publication | Graph Drawing and Network Visualization : 28th International Symposium on Graph Drawing and Network Visualization (GD 2020), Proceedings |
Publication status | E-pub ahead of print - 2020 |
Event | 28th International Symposium on Graph Drawing and Network Visualization: Graph Drawing 2020 - Virtuell, Canada Duration: 16 Sep 2020 → 18 Sep 2020 https://gd2020.cs.ubc.ca/ |
Conference
Conference | 28th International Symposium on Graph Drawing and Network Visualization |
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Country | Canada |
City | Virtuell |
Period | 16/09/20 → 18/09/20 |
Internet address |
Fields of Expertise
- Information, Communication & Computing
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Projects
- 1 Active
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Doctoral Program: Discrete Mathematics
Ebner, O., Thomas, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D. & Berkes, I.
1/05/10 → 31/12/22
Project: Research project