Search results
Results from the WOW.Com Content Network
But if G is a directed acyclic graph (DAG), then no negative cycles can be created, and a longest path in G can be found in linear time by applying a linear time algorithm for shortest paths in −G, which is also a directed acyclic graph. [4] For a DAG, the longest path from a source vertex to all other vertices can be obtained by running the ...
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.
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.
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
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).
A directed acyclic graph is a directed graph that has no cycles. [1] [2] [3] A vertex v of a directed graph is said to be reachable from another vertex u when there exists a path that starts at u and ends at v. As a special case, every vertex is considered to be reachable from itself (by a path with zero edges).
A bipartite graph may be oriented from one side of the bipartition to the other. The longest path in this orientation has length one, with only two vertices. Conversely, if a graph is oriented without any three-vertex paths, then every vertex must either be a source (with no incoming edges) or a sink (with no outgoing edges) and the partition of the vertices into sources and sinks shows that ...
The transitive reduction of a finite directed graph G is a graph with the fewest possible edges that has the same reachability relation as the original graph. That is, if there is a path from a vertex x to a vertex y in graph G, there must also be a path from x to y in the transitive reduction of G, and vice versa. Specifically, if there is ...