Wang's arbitrary cycle-factor conjecture for graphs

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Let GG be a graph of order nn, and let W⊆V(G)W\subseteq V(G) be a vertex set. For a positive integer kk, an arbitrary WW-cycle-factor is a collection of kk disjoint cycles C1,…,CkC_1,\ldots,C_k satisfying ∣V(Ci)∩W∣=ni|V(C_i)\cap W|=n_i for a prescribed partition ∣W∣=n1+⋯+nk|W|=n_1+\cdots+n_k, with each ni≥3n_i\geq 3.

Wang's conjecture. If ∣W∣≥3k|W|\geq 3k and δ(W)≥2n/3\delta(W)\geq 2n/3, then GG contains an arbitrary WW-cycle-factor.

This conjecture generalizes the arbitrary 2-factor theorem of Aigner and Brandt to a specified vertex set. 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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