For n agents with additive valuations, we can find an "EF minus 2" allocation by rounding a connected envy-free cake-cutting, and there…
For n agents with additive valuations, we can find an "EF minus 2" allocation by rounding a connected envy-free cake-cutting, and there also exists an EF2 allocation (proof using a variant of Sperner's lemma).
Open the “Contiguous EF1 allocation” section on Wikipedia →
Source: List of unsolved problems in fair division (CC BY-SA 4.0)