EFX allocations always exist for general monotone valuations in bipartite multigraphs, in multigraphs where each agent has at most ceil(n/4)-1 neighbors, and in multigraphs whose shortest non-parallel cycle has length at least 6.
Fair allocation in graphs
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On the existence of EFX allocations in multigraphs
EFX allocations always exist for general monotone valuations in bipartite multigraphs, in multigraphs where each agent has at most ceil(n/4)-1 neighbors, and in multigraphs whose shortest non-parallel cycle has length at least 6.