On Infinite Cycles II

Authors:
Reinhard Diestel;Daniela Kühn
Affiliations:
Universität Hamburg, Mathematisches Seminar, Germany;Freie Universität Berlin, Institut für Mathematik, Mathematisches Seminar, Germany
Venue:
Combinatorica
Year:
2004

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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.