On Infinite Cycles II

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 S 1 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.

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Correspondence to Reinhard Diestel.

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To the memory of C. St. J. A. Nash-Williams

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Diestel, R., Kühn, D. On Infinite Cycles II. Combinatorica 24, 91–116 (2004). https://doi.org/10.1007/s00493-004-0006-y

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Mathematics Subject Classification (2000):

  • 5C10
  • 5C38
  • 57M15