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Is finding the longest path in a graph an NP-complete problem?

Sanford Balistreri ∙

Lvl 10

∙ 2mo ago

Updated: 2/7/2025

Yes, finding the longest path in a graph is an NP-complete problem.

AnswerBot

∙ 2mo ago

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Continue Learning about Computer Science

What is the complexity of finding the minimum vertex cover in a graph, also known as the vertex cover problem?

The complexity of finding the minimum vertex cover in a graph, also known as the vertex cover problem, is NP-hard.

How does the reduction from clique to independent set demonstrate the relationship between finding a maximum clique in a graph and finding a maximum independent set in the same graph?

Reducing a clique problem to an independent set problem shows that finding a maximum clique in a graph is equivalent to finding a maximum independent set in the same graph. This means that the solutions to both problems are related and can be used interchangeably to solve each other.

What is the dominating set problem and how does it relate to graph theory?

The dominating set problem in graph theory involves finding the smallest set of vertices in a graph such that every other vertex is either in the set or adjacent to a vertex in the set. This problem is important in graph theory as it helps in understanding the concept of domination and connectivity within a graph.

How can the reduction from independent set to vertex cover be used to determine the relationship between the two concepts in graph theory?

The reduction from independent set to vertex cover in graph theory helps show that finding a vertex cover in a graph is closely related to finding an independent set in the same graph. This means that solving one problem can help us understand and potentially solve the other problem more efficiently.

How can the vertex cover problem be reduced to the set cover problem?

The vertex cover problem can be reduced to the set cover problem by representing each vertex in the graph as a set of edges incident to that vertex. This transformation allows us to find a minimum set of sets that cover all the edges in the graph, which is equivalent to finding a minimum set of vertices that cover all the edges in the graph.

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