# 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

## Implementation

(C, Fortran, and Mathematica)

Go to the
Dictionary of Algorithms and Data
Structures home page.

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with Paul Black.

Entry modified 15 July 2019.

HTML page formatted Mon Jul 15 12:55:43 2019.

Cite this as:

Paul E. Black, "vertex cover", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 15 July 2019. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/vertexcover.html