Judiciously 3‐partitioning 3‐uniform hypergraphs. Issue 4 (6th February 2020) - Spink, Hunter; Tiba, Marius
Abstract : Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ℋ with m edges has a vertex‐partition V ()= V 1 ⊔ V 2 ⊔ V 3 such that each part meets at least 1 3 ( 1 − 1 e ) m edges, later improved to 0.6 m by Halsegrave and improved asymptotically to 0.65 m + o ( m ) by Ma and Yu. We improve this asymptotic bound to 19 27 m + o ( m ), which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.