The price of connectivity, the worst-case ratio between the best connected fairness guarantee and the unconstrained one, is 1/k for graphs with a cut vertex that splits into k pieces, at least 3/4 for biconnected graphs with two agents, and 1/(m−n+1) for paths and stars.
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The Price of Connectivity in Fair Division
The price of connectivity, the worst-case ratio between the best connected fairness guarantee and the unconstrained one, is 1/k for graphs with a cut vertex that splits into k pieces, at least 3/4 for biconnected graphs with two agents, and 1/(m−n+1) for paths and stars.