This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are hundreds of such problems known, this list is in no way comprehensive. Many problems of this type can be found in . Graphs and hypergraphs Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). 1-planarity 3-dimensional matching Bandwidth problem Bipartite dimension Capacitated minimum spanning tree Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. Clique cover problem Clique problem Complete coloring, a.k.a. achromatic number Cycle rank Degree-constrained spanning tree Domatic number Dominating set, a.k.a. domination number NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms of the number of edges between parts. Hamiltonian completion Hamiltonian path problem, directed and undirected. Graph intersection number Longest path problem Maximum bipartite subgraph or (especially with weighted edges) maximum cut. Maximum common subgraph isomorphism problem Maximum independent set Maximum Induced path Minimum maximal independent set a.k.a. minimum independent dominating set NP-complete special cases include the minimum maximal matching problem, which is essentially equal to the edge dominating set problem (see above). Metric dimension of a graph Metric k-center Minimum degree spanning tree Minimum k-cut Minimum k-spanning tree Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization Monochromatic triangle Pathwidth, or, equivalently, interval thickness, and vertex separation number Rank coloring k-Chinese postman Shortest total path length spanning tree Slope number two testing Recognizing string graphs Subgraph isomorphism problem Treewidth Testing whether a tree may be represented as Euclidean minimum spanning tree Vertex