MathDBBouchet's 6-flow conjecture for signed graphs
Bouchet's 6-flow conjecture for signed graphs
A signed graph is flow-admissible if it admits a nowhere-zero flow. Bouchet's 6-flow conjecture. Every flow-admissible signed graph has a nowhere-zero 6-flow. This conjecture extends Tutte's 5-flow conjecture from graphs to signed graphs. The paper proves a nowhere-zero 8-flow for every flow-admissible 3-edge-connected signed graph, while the 6-flow conjecture remains open in general.
Sources & referencesView supporting material
Primary source
Matt DeVos, Kathryn Nurse and Robert Šámal, “Nowhere-zero 8-flows in 3-edge-connected signed graphs”, arXiv:2512.18923 (2025).
Additional references
8 papers in this index state this conjecture (2013–2025). The statement above is taken from the most recent of them; the others are arXiv:2310.13504, arXiv:2309.00704, arXiv:1608.06944, arXiv:1601.07813, arXiv:1411.1788, arXiv:1408.1703, arXiv:1307.1562.
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