Univerzalita množin bodů pro alternující hamiltonovské cesty

• Thesis title in Czech: Univerzalita množin bodů pro alternující hamiltonovské cesty
• Thesis title in English: Universality of point sets for alternating Hamiltonian paths
• Key words: geometrický graf|univerzální množina bodů|alternující hamiltonovská cesta
• English key words: geometric graph|universal point set|alternating Hamiltonian path
• Academic year of topic announcement: 2023/2024
• Thesis type: Bachelor's thesis
• Thesis language: čeština
• Department: Department of Applied Mathematics (32-KAM)
• Supervisor: doc. Mgr. Jan Kynčl, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 31.05.2024
• Date of assignment: 03.06.2024
• Confirmed by Study dept. on: 08.01.2025
• Date and time of defence: 11.02.2025 10:30
• Date of electronic submission: 10.01.2025
• Date of submission of printed version: 10.01.2025
• Date of proceeded defence: 11.02.2025
• Opponents: Mgr. Jan Soukup

Guidelines

Úkolem bude pro zadané množiny 2n bodů v rovině zjišťovat, při jakých typech obarvení bodů dvěma barvami existuje alternující hamiltonovská cesta nakreslená pomocí navzájem nekřížících se úseček.

For given sets of 2n points in the plane, the student will investigate for which types of colorings of the points by two colors there is an alternating Hamiltonian path drawn using pairwise noncrossing segments.

References

J. Cibulka, J. Kynčl, V. Mészáros, R. Stolař and P. Valtr, Universal sets for straight-line embeddings of bicolored graphs, in: J. Pach (Ed.), Thirty Essays on Geometric Graph Theory, 101-119, Springer, 2013, ISBN 978-1-4614-0109-4.
A. Kaneko and M. Kano, Discrete Geometry on Red and Blue Points in the Plane - A Survey -, In: Aronov B., Basu S., Pach J., Sharir M. (eds) Discrete and Computational Geometry, Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg, pp 551-570.
M. Kano, J. Urrutia, Discrete geometry on colored point sets in the plane—a survey, Graphs Combin. 37 (2021), no. 1, 1-53.