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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.
Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. [3]: ND25, ND27 Clique cover problem [2] [3]: GT17
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]
In this problem, each variable corresponds to an hour that teacher must spend with cohort , the assignment to the variable specifies whether that hour is the first or the second of the teacher's available hours, and there is a 2-satisfiability clause preventing any conflict of either of two types: two cohorts assigned to a teacher at the same ...
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.
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 ...
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 ...