Minimum codegree conjecture for loose cycle factors

Let nn and tt be integers with n6tn\ge 6t, and let HH be an nn-vertex 3-uniform hypergraph. A loose cycle is a cyclic sequence of edges in which consecutive edges intersect in one vertex and all other pairs of edges are disjoint.

Loose-cycle factor conjecture. If nn is sufficiently large and

δ2(H)2t,\delta_2(H)\ge 2t,

then HH contains tt vertex-disjoint loose cycles.

The source notes that this conjecture would follow trivially from the stronger C6C_6-factor conjecture, since each copy of C6C_6 is a loose cycle.

Sources & referencesView supporting material

Primary source

Wei Gao and Jie Han, “Minimum codegree threshold for C_6^3-factors in 3-uniform Hypergraphs”, arXiv:1508.05152 (2015).

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