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Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...

A sequence of moves (i.e., a path) on a chessboard by a chess piece in which each square of a chessboard is visited exactly once.