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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.
The most prominent examples of covering problems 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 problems allow the covering primitives to overlap; the process of covering something with non-overlapping primitives is called decomposition.
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to the vertex set of G.A covering map f is a surjection and a local isomorphism: the neighbourhood of a vertex v in C is mapped bijectively onto the neighbourhood of in G.
Another problem in subdivision containment is the Kelmans–Seymour conjecture: Every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph K 5. Another class of problems has to do with the extent to which various species and generalizations of graphs are determined by their point-deleted subgraphs ...
The complement of a vertex cover in any graph is an independent set, so a minimum vertex cover is complementary to a maximum independent set; finding maximum independent sets is another NP-complete problem. The equivalence between matching and covering articulated in Kőnig's theorem allows minimum vertex covers and maximum independent sets to ...
Each vertex of the graph is a part of a path, including vertex D, which is a part of a path with length 0. The set of such paths is a path cover. A path cover may also refer to a vertex-disjoint path cover, i.e., a set of paths such that every vertex v ∈ V belongs to exactly one path. [2]
The International Aviation Safety Assessment Program (IASA Program) is a program established by the U.S. Federal Aviation Administration (FAA) in 1992. The program is designed to evaluate the ability of a country's civil aviation authority or other regulatory body to adhere to international aviation safety standards and recommended practices for personnel licensing, aircraft operations and ...
A disjoint cycle cover of an undirected graph (if it exists) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph. [1] [2] If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.