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The problem of finding the longest path or cycle that is an induced subgraph of a given hypercube graph is known as the snake-in-the-box problem. Szymanski's conjecture concerns the suitability of a hypercube as a network topology for communications.
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).
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.
In graph theory terminology, this is called finding the longest possible induced path in a hypercube; it can be viewed as a special case of the induced subgraph isomorphism problem. There is a similar problem of finding long induced cycles in hypercubes, called the coil-in-the-box problem.
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 geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
Routing a permutation of the doubly-directed cube graph. In mathematics, Szymanski's conjecture, named after Ted H. Szymanski (), states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths.
Hypercube graph, a higher-dimensional generalization of the cube graph. 3. Folded cube graph, formed from a hypercube by adding a matching connecting opposite vertices. 4. Halved cube graph, the half-square of a hypercube graph. 5. Partial cube, a distance-preserving subgraph of a hypercube. 6. The cube of a graph G is the graph power G 3.