Bicycles and left–right tours in locally finite graphs

We extend three results involving bicycles and left–right tours to infinite, locally finite graphs: Read and Rosenstiehl’s tripartition theorem, Shank’s theorem that the residues of left–right tours generate the bicycle space and the planarity criterion of Archdeacon, Bonnington and Little. In order to achieve this it is necessary to allow infinite cycles as defined by Diestel and Kühn.