Wang's arbitrary directed W-cycle-factor conjecture

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Let DD be a digraph of order n≥6n\geq 6, and let W⊆V(D)W\subseteq V(D). An arbitrary WW-cycle-factor is a collection of disjoint directed cycles realizing a prescribed partition of ∣W∣|W| into parts of size at least 22.

Wang's conjecture. If δ(W)≥(3n−3)/2\delta(W)\geq (3n-3)/2, then DD contains an arbitrary WW-cycle-factor.

This conjecture generalizes Wang's directed arbitrary cycle-factor conjecture and the graph version for specified vertex sets. Its status is not established in the source.

References

Primary source

Yun Wang and Jin Yan, “On directed version of the Sauer-Spender Theorem”, arXiv:2001.11703 (2020).

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