vertex cover

(classic problem)

Definition: A set of vertices in an undirected graph where every edge connects at least one vertex. The vertex cover problem is to find a minimum size set and is NP-complete.

See also vertex coloring, covering.

Note: An illustration of vertex cover is posting the least number of police to watch every street in a city. Clearly police should be at intersections. What's the smallest set of intersections?

To correspond to the vertex cover problem, streets must be straight. A curving street is divided into segments such that at any intersection, a person can see from that intersection to the next. Also, no street goes straight through an intersection.

Author: PEB


(C, Fortran, and Mathematica)
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Entry modified 2 November 2020.
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Cite this as:
Paul E. Black, "vertex cover", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY) Available from: