Nash-Williams' edge-connectivity orientation conjecture
Nash-Williams' edge-connectivity orientation conjecture
For a natural number , a graph is -edge-connected if every edge cut has size at least , and an orientation is -arc-connected if every ordered pair of vertices is joined by at least edge-disjoint directed paths. Nash-Williams' edge-connectivity orientation conjecture. For any natural number , every -edge-connected graph admits a -arc-connected orientation. This is the edge-connectivity consequence of Nash-Williams' orientation problem for arbitrary graphs. The supplied status evidence says that this problem was answered by Thomas, who proved that one can take ; accordingly, this candidate is recorded as solved.
Sources & referencesView supporting material
Primary source
Leandro Aurichi, Paulo Magalhães Júnior and Guilherme Eduardo Pinto, “On orientations preserving edge-connectivity in infinite graphs”, arXiv:2510.06449 (2025).
Additional references
2 papers in this index state this conjecture (2023–2025). The statement above is taken from the most recent of them; the others are arXiv:2306.10631.
Progress summary
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