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....

graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that set....

Cover. Vertex cover is a special case of Hitting Set. Edge cover is a special case of Set Cover. Geometric set cover is a special case of Set Cover when...

In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed:...

vertex cover. Therefore, the sum of the size of the largest independent set α ( G ) {\displaystyle \alpha (G)} and the size of a minimum vertex cover...

an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs. It was discovered independently, also in...

perfect matching) has a vertex cover of size n + k {\displaystyle n+k} . The odd cycle transversal can be transformed into a vertex cover by including both...

In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. In computer...

In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices...

cover. Hence, these vertices “cover” all the edges. We wish to find a vertex cover that has the smallest possible number of vertices. Vertex covers can...

belonging to the independent set, forms a minimal vertex cover. That is, the complement is a vertex cover, a set of vertices that includes at least one endpoint...

equal in size to the minimum vertex cover. Via this result, the minimum vertex cover, maximum independent set, and maximum vertex biclique problems may be...

labeled 1. cover A vertex cover is a set of vertices incident to every edge in a graph. An edge cover is a set of edges incident to every vertex in a graph...

feedback vertex set (FVS) of a graph is a set of vertices whose removal leaves a graph without cycles ("removal" means deleting the vertex and all edges...

isolated vertex, remove it. An isolated vertex cannot cover any edges, so in this case v {\displaystyle v} cannot be part of any minimal cover. If more...

graph theory, a well-covered graph is an undirected graph in which the minimal vertex covers all have the same size. Here, a vertex cover is a set of vertices...

cover). It is a generalization of the notion of a vertex cover in a graph. The vertex-cover number of a hypergraph H is the smallest size of a vertex...

O(2^{k}m)} . A vertex cover of size k in a graph of order n can be found in time O ( 2 k n ) {\displaystyle O(2^{k}n)} , so the vertex cover problem is also...

where local search has been applied are: The vertex cover problem, in which a solution is a vertex cover of a graph, and the target is to find a solution...

vertices in V ′ {\displaystyle V'} , ie. that V ′ {\displaystyle V'} is a vertex cover of G {\displaystyle G} . Therefore, the size of the boat must be at least...

edges incident to either vertex from the graph. As any vertex cover of the input graph must use a distinct vertex to cover each edge that was considered...

ISSN 0030-364X. Kőnig's theorem (graph theory) Konig's theorem Vertex cover minimum vertex cover Matching (graph theory) matching Bruff, Derek, The Assignment...

hardness of approximation that is known for vertex cover, and the proof uses the Karp–Lawler reduction from vertex cover to feedback arc set, which preserves...

there is no (obvious) relationship between covering graph and vertex cover or edge cover. The combinatorial formulation of covering graphs is immediately...

edge cover is equal to the size of the maximum independent set, and the size of the minimum edge cover plus the size of the minimum vertex cover is equal...

clique covers. The maximum independent set is complementary to a minimum vertex cover, a set of vertices that touches all edges. A minimum clique cover consists...

version) Subgraph isomorphism problem Subset sum problem Clique problem Vertex cover problem Independent set problem Dominating set problem Graph coloring...

this subset. Therefore, the solution describes a vertex cover. Additionally given some vertex cover C, y v {\displaystyle y_{v}} can be set to 1 for any...

are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem. Covering...

one vertex in the cover, then add a new vertex to G, adjacent to this vertex. Each step either takes constant time, or involves finding a vertex cover of...