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Black and White Cycle Conjecture ★★★
Author(s): Arthur; Hoffmann-Ostenhof
Conjecture Let 
be a cubic graph with a nz-
-flow, and let each edge 
satisfying 
does not have a nz--flow be colored black, and let each edge satisfying has a nz--flow be colored white. Then contains a white cycle but not a black cycle.
be a cubic graph with a nz--flow, and let each edge satisfying does not have a nz--flow be colored black, and let each edge satisfying has a nz--flow be colored white. Then contains a white cycle but not a black cycle.
Used terminology: nz--flow is the abbrevation for nowhere-zero -flow, a cycle is a connected 
-regular graph, a cycle is called black (white) if each edge of the cycle is colored black (white).
Keywords: 3-edge-coloring; 4-flow; cubic graphs; removable edge
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