Judiciously 3‐partitioning 3‐uniform hypergraphs
Copyright policy )Judiciously 3‐partitioning 3‐uniform hypergraphs
Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ℋ with m edges has a vertex‐partition V()=V1⊔V2⊔V3 such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.
- Harvard University United States
- Trinity Hall United Kingdom
- International Centre for Mathematical Sciences United Kingdom
Extremal problems in graph theory, judicious partition, concentration inequality, hypergraph, Hypergraphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Azuma-Hoeffding inequality, Mathematics - Combinatorics, Combinatorics (math.CO), optimization, 05C65
Extremal problems in graph theory, judicious partition, concentration inequality, hypergraph, Hypergraphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Azuma-Hoeffding inequality, Mathematics - Combinatorics, Combinatorics (math.CO), optimization, 05C65
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