s, for any given undirected graph G = (V, E), whether there is a way to color each vertex in V with one of the 3 given colors such that no two adjacent vertices have the same color. Show that the 3-colorability is in NP.

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A: To show that a graph lacking articulation points is biconnected, we need to prove that any set of…

Q: A Vertex Cover of an undirected graph G is a subset of the nodes of G, such that every edge of G…

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A: I have answered the question in second step.

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A: The answer is given below:-

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A:

Q: Find the weight of the maximum spanning tree of this graph.

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A: The solution below mention details in step 2

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A: Solution 1: no given any self loop.

Q: An independent set of a graph G = (V, E) is a subset V’ Í V of vertices such that each edge in E is…

A: Answer:  An independent set I of a graph G=(V,E) of V vertice and E edges is the subset of vertices…

Q: Is tme use of Essentially, by processing the vertices in a random order, you can potentially avoid…

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A: please see the next step for solution

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A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…