Nash-Williams’ cycle-decomposition theorem
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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.
Mathematics Subject Classification (2000)05C38 05C40 05C63
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- L. Soukup: Elementary submoduls in infinite combinatorics, arXiv 10007.4309v2 [math.LO] 6.Dec.2010.Google Scholar
- C. Thomassen: Infinite graphs, in: Further Selected Topics in Graph Theory (L. W. Beineke and R. J. Wilson, eds.), Academic Press, London (1983), 129–160.Google Scholar
- C. Thomassen: Orientations of infinite graphs with prescribed edge-connectivity, Combinatorica, to appear.Google Scholar