Berge's five-perfect-matching cover conjecture for bridgeless cubic graphs
Let be a bridgeless cubic graph. A collection of perfect matchings is an edge-covering collection when every edge of belongs to at least one matching in the collection. Berge's conjecture. Every bridgeless cubic graph admits five perfect matchings forming an edge-covering collection. The source states that this conjecture is equivalent to Fulkerson's conjecture and remains open.
References
Primary source
František Kardoš, Edita Máčajová and Jean Paul Zerafa, “Disjoint odd circuits in a bridgeless cubic graph can be quelled by a single perfect matching”, arXiv:2204.10021 (2022).
Additional references
5 papers in this index state this conjecture (2016–2022). The statement above is taken from the most recent of them; the others are arXiv:1807.08138, arXiv:1805.06828, arXiv:1702.07156, arXiv:1601.03248.
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