Máčajová–Škoviera odd-cut conjecture for bridgeless cubic graphs

Let $G$ be a bridgeless cubic graph. A perfect matching is a set of edges meeting every vertex exactly once, and an edge-cut is the set of edges joining a vertex subset to its complement. Máčajová–Škoviera conjecture. Every bridgeless cubic graph has two perfect matchings such that their intersection does not contain an edge-cut of odd cardinality. This is one of the weaker statements implied by the Berge–Fulkerson conjecture and is stated in the source as having been proved by Kardoš, Máčajová and Zerafa.