Seminár z teórie grafov - Martin Škoviera (1.10.2026)
vo štvrtok 1.10.2026 o 9:50 hod. v miestnosti M 213
Prednášajúci: Martin Škoviera
Názov prednášky: Bounding Hamilton cycles in embedded cubic graphs
Termín: 1.10.2026, 9:50 hod., M 213
Abstrakt:
In this talk we develop the idea that embedding a cubic graph into a closed surface can serve as a convenient tool for finding a Hamilton cycle in it. We establish a necessary and sufficient condition for a cubic graph embedded in a closed surface, orientable or not, to have a bounding Hamilton cycle. With this characterisation and its consequences we can guarantee Hamilton cycles in wide classes of cubic graphs. Among others, we can provide a unified and relatively short proof of a result due to Glover, Marusic, Kutnar, and others proved in a series of four papers published over the years 1996-2012 that cubic Cayley graphs of finite quotients of the modular group have a Hamilton path and, except in one special case, they also have a Hamilton cycle. We also show that in the remaining case these graphs have no bounding Hamilton cycle, which indicates that identifying Hamilton cycles for this case is likely to be very difficult.
This is a joint work with Roman Nedela.