Mader's subdivision conjecture for acyclic digraphs
Let be an acyclic digraph, and let denote the minimum out-degree of a digraph . A subdivision of is obtained by replacing the arcs of by directed paths with the same endpoints and internally vertex-disjoint interiors. Mader's subdivision conjecture. For every acyclic digraph there exists a number such that every digraph with
contains a subdivision of . This remains an open problem concerning degree conditions that force directed subdivisions.
References
Primary source
Raphael Steiner, “Openly disjoint cycles and directed tree-width of regular digraphs”, arXiv:2604.13700 (2026).
Additional references
6 papers in this index state this conjecture (2006–2026). The statement above is taken from the most recent of them; the others are arXiv:2603.13955, arXiv:2403.11470, arXiv:2008.13224, arXiv:1801.08249, arXiv:math/0605178.
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