Balanced partitions exist that are O(max{√Δ, k²} ln n)-approximately envy-free and (k + o(k))-approximately core, with efficient computation under relaxed balance and stronger (1.618 + o(1))-core for k=2.
Balanced Graph Partitioning
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Some Improved Results on Fair and Balanced Graph Partitions
Balanced partitions exist that are O(max{√Δ, k²} ln n)-approximately envy-free and (k + o(k))-approximately core, with efficient computation under relaxed balance and stronger (1.618 + o(1))-core for k=2.