The lexicographically first maximal subgraph problems: P-completeness and NC algorithms
The P-completeness of the lexicographically first maximal (l.f.m.) subgraph problem for any nontrivial hereditary property is proved. If the instances are restricted to graphs with degree at most 3, the l.f.m. 4-cycle free subgraph problem is shown to be in NC2. This degree constraint 3 is best possible.
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