Micael Toledo: Cubic graphs with long orbits

Povzetek. For a fixed integer k, we say an automorphism F of a graph has a long orbit if at least 1/k of the vertices of the graph lie in the same orbit under the action of the group generated by F. We give a general overview of cubic graphs admitting an automorphism with a long orbit and we characterize cubic vertex-transitive graphs admitting an automorphism with a long orbit when k=3.