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Geodetic topological cycles in locally finite graphs. (English) Zbl 1230.05219

Summary: We prove that the topological cycle space \(\mathcal C(G)\) of a locally finite graph \(G\) is generated by its geodetic topological circles. We further show that, although the finite cycles of \(G\) generate \(\mathcal C(G)\), its finite geodetic cycles need not generate \(\mathcal C(G)\).

MSC:

05C63 Infinite graphs
05C75 Structural characterization of families of graphs
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