For two agents with monotone valuations, a maximal EF1 allocation of graph-conflicting items always exists for any graph and is efficiently computable; for three or more agents, existence fails and deciding it is NP-hard.
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Dividing Conflicting Items Fairly
For two agents with monotone valuations, a maximal EF1 allocation of graph-conflicting items always exists for any graph and is efficiently computable; for three or more agents, existence fails and deciding it is NP-hard.