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A linear-time algorithm for finding a longest path in a tree was proposed by Edsger Dijkstra around 1960, while a formal proof of this algorithm was published in 2002. [15] Furthermore, a longest path can be computed in polynomial time on weighted trees, on block graphs, on cacti, [16] on bipartite permutation graphs, [17] and on Ptolemaic ...
Grundy number of a directed graph. [3]: GT56 Hamiltonian completion [3]: GT34 Hamiltonian path problem, directed and undirected. [2] [3]: GT37, GT38, GT39 Induced subgraph isomorphism problem; Graph intersection number [3]: GT59 Longest path problem [3]: ND29 Maximum bipartite subgraph or (especially with weighted edges) maximum cut.
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 resulting matrix describes the longest path distances in the graph. Sorting the vertices by the lengths of their longest incoming paths produces a topological ordering. [6] An algorithm for parallel topological sorting on distributed memory machines parallelizes the algorithm of Kahn for a DAG = (,). [7]
Pointer jumping or path doubling is a design technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs. Pointer jumping allows an algorithm to follow paths with a time complexity that is logarithmic with respect to the length of the longest path.
Dijkstra's algorithm finds the shortest path from a given source node to every other node. [7]: 196–206 It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of ...
Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings; Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane; Longest path problem: find a simple path of maximum length in a given graph; Minimum spanning tree. Borůvka's algorithm ...
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.