Maruša Lekše: Consistent cycles in locally finite graphs

Povzetek. A cycle in a graph is called consistent, if there exists an automorphism that acts on it as a 1-step rotation. A theorem by J. H. Conway states that for a finite graph, the number of orbits for the action of the automorphism group on the set of all consistent cycles is equal to the valency of the graph minus one. Later, J. Wessely proved a similar theorem for locally finite graphs in her masters thesis work. In this talk we will present a proof of this result.