Definition
The decision problem is as follows:
- INSTANCE: An (undirected or directed) graph and a positive integer .
- QUESTION: Is there a subset with such that with the vertices from deleted is cycle-free?
The graph that remains after removing from is an induced forest (resp. an induced directed acyclic graph in the case of directed graphs). Thus, finding a minimum feedback vertex set in a graph is equivalent to finding a maximum induced forest (resp. maximum induced directed acyclic graph in the case of directed graphs).
Read more about this topic: Feedback Vertex Set
Famous quotes containing the word definition:
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)