![]() Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph.NP-complete special cases include the minimum maximal matching problem, : GT10 which is essentially equal to the edge dominating set problem (see above). Minimum maximal independent set a.k.a.Maximum common subgraph isomorphism problem : GT49.Maximum bipartite subgraph or (especially with weighted edges) maximum cut.Hamiltonian path problem, directed and undirected.A related problem is to find a partition that is optimal terms of the number of edges between parts. Partition into cliques is the same problem as coloring the complement of the given graph. Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete.NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. Degree-constrained spanning tree : ND1.Variants include the rural postman problem. The program is solvable in polynomial time if the graph has all undirected or all directed edges. Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges).Capacitated minimum spanning tree : ND5.Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Graphs occur frequently in everyday applications. Many problems of this type can be found in Garey & Johnson (1979). As there are hundreds of such problems known, this list is in no way comprehensive. ![]() This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. You can help by adding missing items with reliable sources. This is a dynamic list and may never be able to satisfy particular standards for completeness.
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