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2. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5]

3. Factor graph - Wikipedia

   en.wikipedia.org/wiki/Factor_graph

   with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.

4. Word-representable graph - Wikipedia

   en.wikipedia.org/wiki/Word-representable_graph

   For example, 132-representable graphs are those that can be represented by words w 1 w 2...w n where there are no 1 ≤ a < b < c ≤ n such that w a < w c < w b. In [23] it is shown that any 132-representable graph is necessarily a circle graph, and any tree and any cycle graph, as well as any graph on at most 5 vertices, are 132-representable.

5. 2-factor theorem - Wikipedia

   en.wikipedia.org/wiki/2-factor_theorem

   In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: [ 1 ] Let G {\displaystyle G} be a regular graph whose degree is an even number, 2 k {\displaystyle 2k} .

6. Tree decomposition - Wikipedia

   en.wikipedia.org/wiki/Tree_decomposition

   In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important role in problems like probabilistic inference ...

7. Graph factorization - Wikipedia

   en.wikipedia.org/wiki/Graph_factorization

   The Petersen graph can be partitioned into a 1-factor (red) and a 2-factor (blue). However, the graph is not 1-factorable. In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the ...

8. Euclidean algorithm - Wikipedia

   en.wikipedia.org/wiki/Euclidean_algorithm

   For example, 6 and 35 factor as 6 = 2 × 3 and 35 = 5 × 7, so they are not prime, but their prime factors are different, so 6 and 35 are coprime, with no common factors other than 1. A 24×60 rectangle is covered with ten 12×12 square tiles, where 12 is the GCD of 24 and 60.

9. Generating function - Wikipedia

   en.wikipedia.org/wiki/Generating_function

   6.1.2 Example 2: Modified binomial ... and checking that the result is the constant power series 1 (in other words, ... A spanning tree is a subgraph of a graph which ...