Bang-Jensen and Yeo's strong arc decomposition conjecture
Bang-Jensen and Yeo's strong arc decomposition conjecture
Let be a digraph. It is -arc-strong if remains strong for every subset of size at most . A strong arc decomposition of is a partition of into disjoint sets and such that the spanning subdigraphs and are both strong.
Bang-Jensen and Yeo's conjecture. There exists an integer such that every -arc-strong digraph has a strong arc decomposition.
A strong arc decomposition would imply the existence of a good -pair for every choice of roots, so this conjecture would imply Thomassen's conjecture on good vertex pairs. The source gives no resolution, and the conjecture remains open.
Sources & referencesView supporting material
Primary source
Jiangdong Ai, Yiming Hao, Zhaoxiang Li and Qi Shao, “Arc-disjoint in- and out-branchings in semicomplete split digraphs”, arXiv:2410.12575 (2024).
Additional references
4 papers in this index state this conjecture (2018–2024). The statement above is taken from the most recent of them; the others are arXiv:2302.08283, arXiv:2012.06698, arXiv:1805.01687.
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