Cubic graphs with two odd circuits in a 2-factor and three spokes in the complementary 1-factor admit a cover by four perfect matchings, fulfilling the Alon-Tarsi 7/5-conjecture.
Schönberger,Ein beweis des petersenschen graphensatzes, Acta Scientiarum Mathematicarum (Szeged)7 (1934), 51–57
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On $4$-covers of cubic graphs with two adjacent odd circuits in a $2$-factor
Cubic graphs with two odd circuits in a 2-factor and three spokes in the complementary 1-factor admit a cover by four perfect matchings, fulfilling the Alon-Tarsi 7/5-conjecture.