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2. Seven Bridges of Königsberg - Wikipedia

   en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

   Seven Bridges of Königsberg. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736 [1], laid the foundations of graph theory and prefigured the idea of topology. [2]

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 coloring [2] [3]: GT4 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.

5. Four color theorem - Wikipedia

   en.wikipedia.org/wiki/Four_color_theorem

   In graph-theoretic terms, the theorem states that for loopless planar graph, its chromatic number is ().. The intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color" – needs to be interpreted appropriately to be correct.

6. 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 ...

7. Neighbourhood (graph theory) - Wikipedia

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

   Neighbourhood (graph theory) In this graph, the vertices adjacent to 5 are 1, 2 and 4. The neighbourhood of 5 is the graph consisting of the vertices 1, 2, 4 and the edge connecting 1 and 2. For other meanings of neighbourhoods in mathematics, see Neighbourhood (mathematics). In graph theory, an adjacent vertex of a vertex v in a graph is a ...