(1) Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany;(2) Freie Universität Berlin, Institut für Mathematik, Arnimallee 2–6, 14195 Berlin, Germany
Abstract:
We adapt the cycle space of a finite or locally finite
graph to graphs with vertices of infinite degree, using as
cycles the homeomorphic
images of the unit circle S1 in the
graph together with its ends. We characterize the spanning trees
whose fundamental cycles generate this cycle space, and prove
infinite analogues to the standard characterizations of finite
cycle spaces in terms of edge-decomposition into single cycles
and orthogonality to cuts.To the memory of C. St. J. A.
Nash-Williams