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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 .
Apply dynamic programming to this path decomposition to find a longest path in time (!), where is the number of vertices in the graph. Since the output path has length at least as large as d {\displaystyle d} , the running time is also bounded by O ( ℓ ! 2 ℓ n ) {\displaystyle O(\ell !2^{\ell }n)} , where ℓ {\displaystyle \ell } is the ...
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
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).
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 ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.