Geodetic Topological Cycles in Locally Finite Graphs

Agelos Georgakopoulos, Philipp Sprüssel


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

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