What question did this study set out to answer?

To provide a new proof that 3-uniform hypergraphs with small slicewise VC-dimension allow for ε-homogeneous partitions.

Efficient homogeneous partitions and slicewise VC-dimension

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Randomized trial demonstrates efficient homogeneous partitions in 3-uniform hypergraphs, suggesting new bounds for growth patterns.

To provide a new proof that 3-uniform hypergraphs with small slicewise VC-dimension allow for ε-homogeneous partitions.
Derived new ε-homogeneous partitions of size at most 2^(2^(ε^(-K))), with K being a constant related to VC-dimension.
Developed theoretical proofs based on previous work in hypergraph partitioning.
Achieved explicit bounds for homogeneous partitions in 3-uniform hypergraphs.
Showed that the new proof offers improved clarity and establishes foundational results for subsequent studies.

Caroline Terry (2026) studied this question.

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