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2. Chinese postman problem - Wikipedia

   en.wikipedia.org/wiki/Chinese_postman_problem

   In graph theory, a branch of mathematics and computer science, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed walk that covers every ...

3. Tree (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tree_(graph_theory)

   v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...

4. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   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 ...

5. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles. Other problems specify a family of graphs into which a given graph should be decomposed, for instance, a family of cycles, or decomposing a complete graph K n into n − 1 specified trees ...

6. Shortest path problem - Wikipedia

   en.wikipedia.org/wiki/Shortest_path_problem

   Shortest path problem. Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. [1]

7. Graph isomorphism problem - Wikipedia

   en.wikipedia.org/wiki/Graph_isomorphism_problem

   The graph isomorphism problem is computationally equivalent to the problem of computing the automorphism group of a graph, [17][18][19] and is weaker than the permutation group isomorphism problem and the permutation group intersection problem. For the latter two problems, Babai, Kantor & Luks (1983) obtained complexity bounds similar to that ...