The authors establish NP-hardness for recovering optimal colorings from one-vertex-deleted subgraphs even with one-edge-deleted solutions given, polynomial-time solvability from one-edge-added supergraphs, and new DP- and Theta_2^p-completeness results for minimality and criticality problems.
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Finding Optimal Solutions With Neighborly Help
The authors establish NP-hardness for recovering optimal colorings from one-vertex-deleted subgraphs even with one-edge-deleted solutions given, polynomial-time solvability from one-edge-added supergraphs, and new DP- and Theta_2^p-completeness results for minimality and criticality problems.