On several partitioning problems of Bollobás and Scott

@article{Ma2010OnSP,
title={On several partitioning problems of Bollob{\'a}s and Scott},
author={Jie Ma and Pei-Lan Yen and Xingxing Yu},
journal={J. Comb. Theory, Ser. B},
year={2010},
volume={100},
pages={631-649}
}

Judicious partition problems on graphs and hypergraphs ask for partitions that optimize several quantities simultaneously. Let G be a hypergraph with m1 edges of size i for i = 1, 2. We show that for any integer k ≥ 1, V (G) admits a partition into k sets each containing at most m1/k + m2/k 2 + o(m2) edges, establishing a conjecture of Bollobás and Scott. We also prove that V (G) admits a partition into k ≥ 3 sets, each meeting at least m1/k+m2/(k−1)+o(m2) edges, which for large graphs implies… CONTINUE READING