A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf
.
Envy-free Matchings in Bipartite Graphs and their Applications to Fair Division
[article]
2021
arXiv
pre-print
A matching in a bipartite graph with parts X and Y is called *envy-free* if no unmatched vertex in X is a adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do not. We prove that every bipartite graph has a unique partition such that all envy-free matchings are contained in one of the partition sets. Using this structural theorem, we provide a polynomial-time algorithm for finding an envy-free matching of maximum
arXiv:1901.09527v5
fatcat:v5kaknb56rcs7dafstho36azte