Qinghou Zeng

Resolving long-standing conjectures, this work proves tight bounds for judicious graph and hypergraph partitions, showing that optimal edge coverage is achievable even with multiple partitions.

Melnikov's valency-variety problem is solved, revealing that the chromatic number is bounded by a specific function of graph size and degree diversity, with constructions proving these bounds are tight.

The optimal $O(m^{2/3})$ error term for partitioning 3-uniform hypergraphs is finally established, improving upon previous bounds.