• Corpus ID: 246210171

Fixed-point cycles and EFX allocations

@article{Berendsohn2022FixedpointCA,
  title={Fixed-point cycles and EFX allocations},
  author={Benjamin Aram Berendsohn and Simona Boyadzhiyska and L{\'a}szl{\'o} Kozma},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.08753}
}
We study edge-labelings of the complete bidirected graph ↔ Kn with functions from the set [d] = {1, . . . , d} to itself. We call a cycle in ↔ Kn a fixed-point cycle if composing the labels of its edges results in a map that has a fixed point, and we say that a labeling is fixed-point-free if no fixed-point cycle exists. For a given d, we ask for the largest value of n, denoted Rf (d), for which there exists a fixed-point-free labeling of ↔ Kn. Determining Rf (d) for all d > 0 is a natural… 
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