Vertex Cover Number

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G).

The König-Egeváry theorem states that the matching number (i.e., size of a maximum independent edge set) and vertex cover number are equal for a bipartite graph.

The independence number alpha(G) of a graph G and vertex cover number are related by


where n=|G| is the vertex count (West 2000).

See also

Independence Number, Minimum Vertex Cover, Vertex Cover, Vertex Cover Polynomial

Explore with Wolfram|Alpha


West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.

Cite this as:

Weisstein, Eric W. "Vertex Cover Number." From MathWorld--A Wolfram Web Resource.

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