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Turn-by-turn navigation is a feature of some satellite navigation devices where directions for a selected route are continually presented to the user in the form of spoken or visual instructions. [1] The system keeps the user up-to-date about the best route to the destination, and is often updated according to changing factors such as traffic ...
Turán's theorem states that the Turán graph has the largest number of edges among all Kr+1 -free n -vertex graphs. Turán's theorem, and the Turán graphs giving its extreme case, were first described and studied by Hungarian mathematician Pál Turán in 1941. [1] The special case of the theorem for triangle-free graphs is known as Mantel's ...
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of (the complete graph on five vertices) or of (a complete bipartite graph on six vertices, three ...
Pursuit–evasion. Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. [1]
A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).
Among directed graphs, the oriented graphs are the ones that have no 2-cycles (that is at most one of (x, y) and (y, x) may be arrows of the graph). [1] A tournament is an orientation of a complete graph. A polytree is an orientation of an undirected tree. [2] Sumner's conjecture states that every tournament with 2n – 2 vertices contains ...
The Dubins path is commonly used in the fields of robotics and control theory as a way to plan paths for wheeled robots, airplanes and underwater vehicles. There are simple geometric [8] and analytical methods [9] to compute the optimal path. For example, in the case of a wheeled robot, a simple kinematic car model (also known as Dubins' car ...
If G is a graph, the line graph L(G) has a vertex for each edge of G, and an edge for each pair of adjacent edges in G. Thus, the chromatic number of L(G) equals the chromatic index of G. If G is bipartite, the cliques in L(G) are exactly the sets of edges in G sharing a common endpoint. Now Kőnig's line coloring theorem, stating that the ...