Fan–Raspaud conjecture for bridgeless cubic graphs
Let be a bridgeless cubic graph. Fan–Raspaud conjecture. The graph contains three perfect matchings such that no edge is covered by all three of them. The Berge–Fulkerson conjecture implies this conjecture, but the Fan–Raspaud conjecture remains open, including in the finite setting discussed in the source.
References
Primary source
Paulo Magalhães Júnior and Antonio Kelson Silva, “On some perfect matching conjectures in infinite, cubic, bridgeless graphs”, arXiv:2607.29511 (2026).
Additional references
7 papers in this index state this conjecture (2012–2026). The statement above is taken from the most recent of them; the others are arXiv:2206.10975, arXiv:1805.06828, arXiv:1702.07156, arXiv:1601.05762, arXiv:1501.00860, arXiv:1209.4510.
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