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.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
J. A. Bondy and U. S. R. Murty: Graph Theory with Applications, The MacMillan Press Ltd. (1976).
R. Diestel: Graph Theory, Springer Verlag (1997) and 4th edition (2010).
F. Jaeger: Flows and Generalized Coloring Theorems in Graphs, Journal of Combinatorial Theory, Series B 26 (1979), 205–216.
F. Laviolette: Decompositions of infinite Graphs: I- bond-faithful decompositions, Journal of Combinatorial Theory, Series B 94 (2005), 259–277.
F. Laviolette: Decompositions of infinite Graphs: II- circuit decompositions, Journal of Combinatorial Theory, Series B 94 (2005), 278–333.
C. St. J. A. Nash-Williams: Decomposition of graphs into closed and endless chains, Proc. London Math. Soc. 3 (1960), 221–238.
C. St. J. A. Nash-Williams: Infinite graphs- a survey, J. Combin. Theory 3 (1967), 286–301.
L. Soukup: Elementary submoduls in infinite combinatorics, arXiv 10007.4309v2 [math.LO] 6.Dec.2010.
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.
C. Thomassen: Orientations of infinite graphs with prescribed edge-connectivity, Combinatorica, to appear.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research partly supported by ERC Advanced Grant GRACOL.
