Gabriel Verret (FMF UL, Slovenija): 4-valent arc-transitive graphs with large vertex-stabilisers

Povzetek: A classical result of Tutte is that, in a 3-valent arc-transitive graphs, a vertex-stabiliser has order at most 48. On the other hand, 4-valent arc-transitive graphs can have arbitrarily large vertex-stabilisers, hence there is no equivalent to Tutte's theorem in the 4-valent case. Instead, we consider the order of a vertex-stabiliser as a function of the number of vertices of such a graph and discuss some interesting upper bounds on this function.