Tutte made the conjecture in 1966 that every 2-connected cubic graph not containing the Petersen graph as a minor is 3-edge-colourable. The conjecture is still open, but we show that it is true, in general, provided it is true for two special kinds of cubic graphs that are almost planar. © 1997 Academic Press.
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Robertson, N., Seymour, P., & Thomas, R. (1997). Tutte’s edge-colouring conjecture. Journal of Combinatorial Theory. Series B, 70(1), 166–183. https://doi.org/10.1006/jctb.1997.1752