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).
A dual form of the problem is called the Fulkerson conjecture.
Archdeacon, D. "The Cycle Double Cover Conjecture." http://www.cems.uvm.edu/~archdeac/problems/cyclecov.htm.Goddyn,
L. "Cycle Covers of Graphs." Ph.D. thesis. Waterloo, Ontario, Canada: University
of Waterloo.Jaeger, F. "A Survey of the Cycle Double Cover Conjecture."
In Cycles in Graphs (Ed. B. Alspach and C. D. Alspach). North
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).
New York: Academic Press, pp. 341-355, 1979.Szekeres, G. "Polyhedral
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.
