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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.
An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem. Similarly, an induced cycle is a cycle that is an induced subgraph of G ; induced cycles are also called chordless cycles or (when the length of the cycle is four or more) holes .
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
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.
A path such that no graph edges connect two nonconsecutive path vertices is called an induced path. A path that includes every vertex of the graph without repeats is known as a Hamiltonian path. Two paths are vertex-independent (alternatively, internally disjoint or internally vertex-disjoint) if they do not have any internal vertex or edge in ...
The theory of the world’s “longest rail ride” originated when the Laos-China railway opened for business, linking Kunming and Vientiane – a missing link in the rails between Europe and ...
Each section will be 217 meters long (roughly half the length of the world’s largest container ship), 42 meters wide and 9 meters tall. Weighing in at 73,000 metric tons each, they will be as ...
A Hamiltonian path or traceable path is a path that visits each vertex of the graph exactly once. A graph that contains a Hamiltonian path is called a traceable graph. A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices.