Search results
Results from the WOW.Com Content Network
Example graph that has a vertex cover comprising 2 vertices (bottom), but none with fewer. In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem.
A vertex cover is a special case of a fractional vertex cover in which all weights are either 0 or 1. The size of a fractional vertex-cover is the sum of fractions of all vertices. The fractional vertex-cover number of a hypergraph H is the smallest size of a fractional vertex-cover in H. It is often denoted by τ*(H).
In the above example, each vertex of H has exactly 2 preimages in C. Hence C is a 2-fold cover or a double cover of H. For any graph G, it is possible to construct the bipartite double cover of G, which is a bipartite graph and a double cover of G. The bipartite double cover of G is the tensor product of graphs G × K 2:
An example of a bipartite graph, with a maximum matching (blue) and minimum vertex cover (red) both of size six. In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (), describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs.
Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases ... Vertex cover [2] [3]: GT1 ...
The vertex-cover number of a hypergraph H is the smallest size of a vertex cover in H. It is often denoted by τ(H), [1]: 466 for transversal. A fractional vertex-cover is a function assigning a weight to each vertex in V, such that for every hyperedge e in E, the sum of fractions of vertices in e is at least 1. A vertex cover is a special case ...
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
That is, the complement is a vertex cover, a set of vertices that includes at least one endpoint of each edge, and is minimal in the sense that none of its vertices can be removed while preserving the property that it is a cover. Minimal vertex covers have been studied in statistical mechanics in connection with the hard-sphere lattice gas ...