Final answer:
The related decision problem for the independent-set problem is deciding whether a given graph contains an independent set of size k or more, known as the Maximal Independent Set problem, a well-known NP-complete problem.
Step-by-step explanation:
When formulating a related decision problem for the independent-set problem, one must understand the context of the term 'independent set' within graph theory. An independent set is a set of vertices in a graph, no two of which are adjacent. This means that no vertices in the set should share an edge.
The decision problem that can be related to the independent-set problem could be framed as follows: 'Given a graph G and an integer k, does G contain an independent set of size k or more?' This is known as the Maximal Independent Set problem, which is a common problem in computer science and graph theory.
To find the solution, you need to:
- Identify the given information: - We're given a graph G and a number k.
- Determine what the problem is asking you to find: - We need to decide whether there is an independent set of at least size k in the graph G.
This problem is NP-complete, meaning that it is as hard as the hardest problems in NP (nondeterministic polynomial time) classes and there is no known polynomial-time solution.