Seminar of Graph Theory - Matúš Matok (16.5.2024)
Thursday 16.5.2024 at 9:50, Lecture room C
Matúš Matok:
Towards the smallest signed planar non-4-colourable graph
Abstract:
In 2019, Kardoš and Narboni constructed a counterexample to the 4-colour theorem for signed planar graphs, proposed as a conjecture by Máčajová, Raspaud and Škoviera in 2016. This counterexample consisted of gadgets with significant properties. Gadgets, in the form of tripoles, became the area of our interest. Therefore, we introduced a classification of tripoles and set out to find the smallest representative of each class. In this talk, we will discuss the details of the exhaustive search for these representatives.