Search results
Results from the WOW.Com Content Network
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs.
The clique cover number of a graph G is the smallest number of cliques of G whose union covers the set of vertices V of the graph. A maximum clique transversal of a graph is a subset of vertices with the property that each maximum clique of the graph contains at least one vertex in the subset. [2]
Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. [1] However certain other cases of subgraph isomorphism may be solved in polynomial time. [2] Sometimes the name subgraph matching is also used for the same problem ...
It is possible to find the maximum clique, or the clique number, of an arbitrary n-vertex graph in time O (3 n/3) = O (1.4422 n) by using one of the algorithms described above to list all maximal cliques in the graph and returning the largest one. However, for this variant of the clique problem better worst-case time bounds are possible.
The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph can be found as an induced subgraph of another. Because it includes the clique problem as a special case, it is NP-complete .
In one direction, the Hamiltonian path problem for graph G can be related to the Hamiltonian cycle problem in a graph H obtained from G by adding a new universal vertex x, connecting x to all vertices of G. Thus, finding a Hamiltonian path cannot be significantly slower (in the worst case, as a function of the number of vertices) than finding a ...
A d-claw in a graph is a set of d+1 vertices, one of which (the "center") is connected to the other d vertices, but the other d vertices are not connected to each other. A d-claw-free graph is a graph that does not have a d-claw subgraph. Consider the algorithm that starts with an empty set, and incrementally adds an arbitrary vertex to it as ...
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.