# minimum vertex set removal for edge-free graph

I'd like to know the name and the algorithm for the following problem which I'm guessing is a classic, but is slightly different from graph connectivity.

Consider a undirected graph G=(V,E). What is the minimum number of vertices which removal (vertices and their adjacent edges) makes the resulting sub-graph empty of any edge?

For example: If A - B - C, then just need to remove B. If A - B - C and A - C, then need to remove at two vertices (any pair).

For an algo, intuitively I'd proceed by removing first the vertex of highest degree and proceed the same on the remaining graph until there are no edges. Not sure if it gives the min number. For sure, in the worst case I can always go through all possible |V|! removal possibilities and take the min.

• Welcome to Computer Science! Note that you can use LaTeX here to typeset mathematics in a more readable way. See here for a short introduction. Sep 16, 2014 at 13:39
• Can you clarify what you mean by "makes the resulting sub-graph empty of any edge?" Do you mean, the minimum number of vertices whose removal leaves a graph with no remaining edges?
– D.W.
Sep 16, 2014 at 22:36