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An induced path of length four in a cube.Finding the longest induced path in a hypercube is known as the snake-in-the-box problem.. In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G.
Induced subgraph isomorphism problem; Graph intersection number [3]: GT59 Longest path problem [3]: ND29 Maximum bipartite subgraph or (especially with weighted edges) maximum cut. [2] [3]: GT25, ND16 Maximum common subgraph isomorphism problem [3]: GT49 Maximum independent set [3]: GT20 Maximum Induced path [3]: GT23
The path should never travel to a corner which has been marked unusable. In other words, a snake is a connected open path in the hypercube where each node connected with path, with the exception of the head (start) and the tail (finish), it has exactly two neighbors that are also in the snake. The head and the tail each have only one neighbor ...
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
The shortest path between any two vertices in an unweighted graph is always an induced path, because any additional edges between pairs of vertices that could cause it to be not induced would also cause it to be not shortest. Conversely, in distance-hereditary graphs, every induced path is a shortest path. [2]
In two dimensions, the chordal metric on the sphere is not intrinsic, and the induced intrinsic metric is given by the great-circle distance. Every connected Riemannian manifold can be turned into a path metric space by defining the distance of two points as the infimum of the lengths of continuously differentiable curves connecting the two ...