Partitioning 3-uniform hypergraphs

Authors:
Jie Ma;Xingxing Yu
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA;School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 5
Cited 1

Judicious partitions of hypergraphs

Journal of Combinatorial Theory Series A
Judicious partitions of 3-uniform hypergraphs

European Journal of Combinatorics
Problems and results on judicious partitions

Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Maximum cuts and judicious partitions in graphs without short cycles

Journal of Combinatorial Theory Series B
On several partitioning problems of Bollobás and Scott

Journal of Combinatorial Theory Series B

Bisections of graphs

Journal of Combinatorial Theory Series B

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Abstract

Bollobas 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 at least rm/(2r-1) edges. For r=3, Bollobas, Reed and Thomason proved the lower bound (1-1/e)m/3~0.21m, which was improved to (5/9)m by Bollobas and Scott and to 0.6m by Haslegrave. 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 0.65m-o(m) edges.