Minimum codegree conjecture for loose cycle factors
Minimum codegree conjecture for loose cycle factors
Let and be integers with , and let be an -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 is sufficiently large and
then contains vertex-disjoint loose cycles.
The source notes that this conjecture would follow trivially from the stronger -factor conjecture, since each copy of 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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