Tutte's three-edge-coloring conjecture for cubic graphs without a Petersen minor

Let $G$ be a $2$-connected cubic graph with no Petersen minor. A proper three-edge-coloring assigns one of three colors to each edge so that edges incident with the same vertex receive different colors. Tutte's conjecture. Every $2$-connected cubic graph with no Petersen minor is 3-edge colorable. The conjecture extends the four color theorem beyond planar graphs and implies three-edge-colorability for several classes of non-planar cubic graphs. It was eventually settled by a series of papers using the classical proof method of the four color theorem.