On the hamiltonicity of line graphs of locally finite, 6-edge-connected graphs
Journal of Graph Theory
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Bonnington and Richter defined the cycle space of an infinitegraph to consist of the sets of edges of subgraphs having evendegree at every vertex. Diestel and Kühn introduced adifferent cycle space of infinite graphs based on allowing infinitecircuits. A more general point of view was taken by Vella andRichter, thereby unifying these cycle spaces. In particular,different compactifications of locally finite graphs yielddifferent topological spaces that have different cycle spaces. Inthis work, the Vella-Richter approach is pursued by consideringcycle spaces over all fields, not just ℤ2. Inorder to understand "orthogonality" relations, it is helpful toconsider two different cycle spaces and three different bondspaces. We give an analog of the "edge tripartition theorem" ofRosenstiehl and Read and show that the cycle spaces of differentcompactifications of a locally finite graph are related. ©2008 Wiley Periodicals, Inc. J Graph Theory 59: 162176, 2008