In this paper, we show that any 3-uniform hypergraph with m edges can be partitioned into 3 sets, each of which meets at least 0.65 m − o ( m ) edges.
Abstract. Bollobás and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges can be partitioned into r sets so that each set meets ...
Abstract. A conjecture of Bollobás and Thomason asserts that, for r ≥ 1, every r-uniform hypergraph with m edges can be parti-.
Introduction. Judicious partitioning problems seek to partition the vertices of a hy- pergraph H with m edges such that various quantities are ...
Feb 6, 2020 · 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 ...
Oct 3, 2018 · Abstract:Bollobás, Reed and Thomason proved every 3-uniform hypergraph \mathcal{H} with m edges has a vertex-partition V(\mathcal{H})=V_1 ...
Apr 18, 2022 · In this paper we show that if a 3-uniform hypergraph H has VC_2-dimension at most k, then there is a regular partition \mathcal{P} for H of complexity (t,\ell).
Abstract. The regularity method was pioneered by Szemerédi for graphs and is an important tool in extremal combinatorics. Over the last two decades, ...
Abstract. The main results of this paper are regularity and counting lemmas for 3- uniform hypergraphs. A combination of these two results gives a new proof ...
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May 29, 2024 · For a fixed -uniform hypergraph , these regularity lemmata provide well-structured partitions of where for most edges , the hypergraph is ...