The Feedback Vertex Set problem is defined as follows: Given: a graph G and a positive integer k Question: does G have a set S of at most k vertices such that the subgraph induced by the complement of S is acyclic? In other words, the problem asks whether deleting at most k vertices from a graph makes it acyclic. Assume you found a trusted polynomial-time algorithm, A, for the decision version of the problem. Write a polynomial-time algorithm that uses A to solve the search version. 2. Answer the same question for the Graph Coloring problem.
The Feedback Vertex Set problem is defined as follows: Given: a graph G and a positive integer k Question: does G have a set S of at most k vertices such that the subgraph induced by the complement of S is acyclic? In other words, the problem asks whether deleting at most k vertices from a graph makes it acyclic. Assume you found a trusted polynomial-time algorithm, A, for the decision version of the problem. Write a polynomial-time algorithm that uses A to solve the search version. 2. Answer the same question for the Graph Coloring problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Feedback Vertex Set problem is defined as follows:
Given: a graph G and a positive integer k
Question: does G have a set S of at most k vertices such that the subgraph induced
by the complement of S is acyclic?
In other words, the problem asks whether deleting at most k vertices from a graph
makes it acyclic.
Assume you found a trusted polynomial-time algorithm, A, for the decision version
of the problem. Write a polynomial-time algorithm that uses A to solve the search
version.
2. Answer the same question for the Graph Coloring problem.
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