The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together contain every edge exactly twice.
This conjecture remains open, and was independently formulated by Szekeres (1973)
and Seymour (1979).

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of Waterloo.Jaeger, F. "A Survey of the Cycle Double Cover Conjecture."
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Holland, pp. 1-12, 1985.Seymour, P. D. "Sums of Circuits."
In Graph Theory and Related Topics (Ed. J. A. Bondy and U. R. S. Murty).
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Decompositions of Cubic Graphs." Bull. Austral. Math. Soc.8,
367-387, 1973.West, D. "Cycle Double Cover Conjecture (1978/1979)."
http://www.math.uiuc.edu/~west/openp/cdc.html.