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.

Q: 2 1 3) y=-(x– 4)³ + 2(x – 4) ³ 5 Graph showing all algorithm and work

A: We can proceed as follows

Q: Draw an undirected weighted graph with at least 10 vertices. Edge weights must be different. Perform…

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Q: Use the critical path algorithm to create a priority list for the digraph below. T1 (2) T4 (12) Т6…

A: To find- Use the critical path algorithm to create a priority list for the diagraph below. Priority…

Q: B A 13 AFBECDA 5. X Question Help: Post to forum Submit Question 14 Apply the sorted edges algorithm…

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Q: d) Find a minimal spanning tree in the following weighted graph using the Prim's algorithm. V7 V6 V4…

A: As per the Prim's algorithm first in the given graph G, we need to remove the loops and parallel…

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Q: Now consider an arbitrary graph G. Give a polynomial-time algorithm to determine whether G is a…

A: To determine whether a given graph G is a tree or not, you can use a polynomial-time algorithm based…

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A: A chicken farmer wishes to provide electric power to each chicken house on his farm by installing…

Q: a b e d

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Q: 14 10. E 13 Apply the sorted edges algorithm to the graph above. Give your answer as a list of…

A: By using sorted edges algorithm we find the Hamiltonian circuit in given graph:

Q: Given the directed graph: H A B G F E Using the algorithm from the Content, list the vertices in the…

A: To solve this problem, we can use the following depth-first search (DFS) algorithm.

Q: 2. Prove that any graph has at least two vertices with the same degree. A complete bipartite graph…

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Q: The definition of weighted graph is such that every edge has positive weight. If the def- inition…

A: Approach to solving the question: Kruskal's algorithm:Kruskal's algorithm works by greedily…

Q: Apply Dijkstra's algorithm for the following graph. Show the values for p and IN and the d values…

A: Finally we visit all the nodes. Column 1 contains the nodes in order in which we want to traverse.…

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A: the shortest path from g to a is (g,e,d,b,a)=13 option d is correct answer

Q: 1. Find the shortest path between a and h in the weighted graphs given. Show all the work procedures…

A: Given weighted graph is Dijkstra's algorithm solve the single source shortest path problem.

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.