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2. Turn-by-turn navigation - Wikipedia

   en.wikipedia.org/wiki/Turn-by-turn_navigation

   Turn-by-turn systems typically use an electronic voice to inform the user whether to turn left or right, the street name, and the distance to the next turn. [ 3 ] Mathematically, turn by turn navigation is based on the shortest path problem within graph theory , which examines how to identify the path that best meets some criteria (shortest ...

3. Pursuit–evasion - Wikipedia

   en.wikipedia.org/wiki/Pursuit–evasion

   Several variants are equivalent to important graph parameters. Specifically, finding the number of pursuers necessary to capture a single evader with infinite velocity in a graph G (when pursuers and evader are not constrained to move turn by turn, but move simultaneously) is equivalent to finding the treewidth of G, and a winning strategy for the evader may be described in terms of a haven in G.

4. 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 ...

5. Dual graph - Wikipedia

   en.wikipedia.org/wiki/Dual_graph

   Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in turn generalized combinatorially by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces.

6. Maze-solving algorithm - Wikipedia

   en.wikipedia.org/wiki/Maze-solving_algorithm

   Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.

7. Turán's theorem - Wikipedia

   en.wikipedia.org/wiki/Turán's_theorem

   In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...