We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut. We also prove that every bridgeless graph has a collection of cycles covering each edge at least once and at most 7 times. The two results are equivalent in the sense that each can be derived from the other.
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Research partly supported by ERC Advanced Grant GRACOL.
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Thomassen, C. Nash-Williams’ cycle-decomposition theorem. Combinatorica 37, 1027–1037 (2017). https://doi.org/10.1007/s00493-016-3424-8
Mathematics Subject Classification (2000)