Nash-Williams’ cycle-decomposition theorem

Article

Abstract

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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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkLyngbyDenmark

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