# 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 polices 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.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 2 September 2014.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "vertex cover", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2014. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/vertexcover.html