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What (who) is Hamiltonian problem - definition

THEORETICAL PROBLEM IN GRAPH THEORY

Hamiltonian cycle problem; Directed Hamiltonian circuit problem; Hamilton path problem; Hamiltonian Path Problem; Directed Hamiltonian cycle problem; Algorithms for solving the Hamiltonian path problem

Hamiltonian problem

<computability> (Or "Hamilton's problem") A problem in {graph theory} posed by William Hamilton: given a graph, is there a path through the graph which visits each vertex precisely once (a "Hamiltonian path")? Is there a Hamiltonian path which ends up where it started (a "Hamiltonian cycle" or "Hamiltonian tour")? Hamilton's problem is NP-complete. It has numerous applications, sometimes completely unexpected, in computing. http://ing.unlp.edu.ar/cetad/mos/Hamilton.html. (1997-07-18)

Hamiltonian path problem

In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete.

https://en.wikipedia.org/wiki/Hamiltonian_path_problem

Hamiltonian (control theory)

FUNCTION USED IN OPTIMAL CONTROL THEORY

Current value Hamiltonian; Present value Hamiltonian

The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period.

https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)

Wikipedia

Hamiltonian path problem

In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete.

The Hamiltonian cycle problem is a special case of the travelling salesman problem, obtained by setting the distance between two cities to one if they are adjacent and two otherwise, and verifying that the total distance travelled is equal to n (if so, the route is a Hamiltonian circuit; if there is no Hamiltonian circuit then the shortest route will be longer).

https://en.wikipedia.org/wiki/Hamiltonian path problem