The cycle space of a 3-connected locally finite graph is generated by its finite and infinite peripheral circuits

摘要

We extend Tutte's result that in a finite 3-connected graph the cycle space is generated by the peripheral circuits to locally finite graphs. Such a generalization becomes possible by the admission of infinite circuits in the graph compactified by its ends. (C) 2004 Henning Bruhn. Published by Elsevier (USA). All rights reserved.