Projects per year
Abstract
Károlyi, Pach, and Tóth proved that every 2edgecolored straightline 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 kedgecolored, 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⌉edgecolored monotone simple drawing of Kn contains a hypochromatic plane spanning tree. (In a monotone drawing, every edge is represented as an xmonotone curve.)
Original language  English 

Title of host publication  Graph Drawing and Network Visualization : 28th International Symposium on Graph Drawing and Network Visualization (GD 2020), Proceedings 
Publication status  Epub 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 

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

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., SavaHuss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D. & Berkes, I.
1/05/10 → 31/12/22
Project: Research project