Draganić–Keevash–Müyesser conjecture on induced KrK_r-factors

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Let r≥2r\geq 2, and let GG be an ((r−1)n+1)((r-1)n+1)-regular graph on rnrn vertices. A subset S⊆V(G)S\subseteq V(G) is said to induce a KrK_r-factor when G[S]G[S] contains a collection of vertex-disjoint copies of KrK_r covering all vertices of G[S]G[S]. Draganić–Keevash–Müyesser conjecture. There is a constant c>0c>0 such that at least c2rnc2^{rn} subsets of V(G)V(G) induce a KrK_r-factor. The conjecture is resolved by the result stated in the paper for sufficiently large nn, while the abstract says that this confirms the conjecture for large nn.

References

Primary source

Wanting Sun, Shunan Wei and Donglei Yang, “Clique factors in random samplings of regular graphs”, arXiv:2512.20287 (2025).

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