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

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....

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...

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...

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

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...

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...

common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite...

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...

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...

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...

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

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...

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...

such previously known solutions for special cases of satisfiability, vertex cover, and other graph problems. They have received notable coverage due to...

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...

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...

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...

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...

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...

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...

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

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

neighborhoods. Vertex cover problem is the special case of set cover problem where sets to cover are every edges. The original set cover problem, also...

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...

G = (V, E), a path cover is a set of directed paths such that every vertex v ∈ V belongs to at least one path. Note that a path cover may include paths...

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...

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...