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Graph homomorphism problem [3]: GT52 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 ...
The next example is about regular graphs. WLtest cannot distinguish regular graphs of equal order, [4]: 31 but WLpair can distinguish regular graphs of distinct degree even if they have the same order. In fact WLtest terminates after a single round as seen in these examples of order 8, which are all 3-regular except the last one which is 5-regular.
The special case of finding a long path as an induced subgraph of a hypercube has been particularly well-studied, and is called the snake-in-the-box problem. [3] The maximum independent set problem is also an induced subgraph isomorphism problem in which one seeks to find a large independent set as an induced subgraph of a larger graph, and the maximum clique problem is an induced subgraph ...
The Subgraph Isomorphism problem is NP-complete. The graph isomorphism problem is suspected to be neither in P nor NP-complete, though it is in NP. This is an example of a problem that is thought to be hard, but is not thought to be NP-complete. This class is called NP-Intermediate problems and exists if and only if P≠NP.
Graphs are commonly used to encode structural information in many fields, including computer vision and pattern recognition, and graph matching, i.e., identification of similarities between graphs, is an important tools in these areas. In these areas graph isomorphism problem is known as the exact graph matching. [47]
A psychometric function is an inferential psychometric model applied in detection and discrimination tasks. It models the relationship between a given feature of a physical stimulus , e.g. velocity, duration, brightness, weight etc., and forced-choice responses of a human or animal test subject.
Since the clique problem is NP-complete, this polynomial-time many-one reduction shows that subgraph isomorphism is also NP-complete. [3] An alternative reduction from the Hamiltonian cycle problem translates a graph G which is to be tested for Hamiltonicity into the pair of graphs G and H, where H is a cycle having the same number of vertices ...
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...