Homework Answers
Given trouble is NP-complete.
To show any problem is thought to be NP-complete.
It has to create happy two conditions:
1) The clique difficulty is in NP
2) There exists an NP-complete reducible to a clique trouble.
1)consider a place with n number of rudiments has 2^n number of subsets.
graph with n amount of vertices has 2^n number of achievable subgraphs.for checking clique in each sub graph takes exponential occasion by deterministic mechanism.
That income it is not in P
2) reduce a 3SAT predicament to the NP form.A 3 SAT predicament has a solution ,if the resultant vertices form a faction.
That means we are capable to reduce the 3SAT crisis to clique problem, then clique problem is NP-complete.
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2. For a given graph G, we say that H is a clique if H is a complete subgraph of Design an algori...
2. For a given graph G, we say that H is a clique if H is a complete subgraph of Design an algorithm such that if given a graph G and an integer k as input, determines whether or not G has a clique with k vertices in polynomial time. (Hint: Try to first find a polynomial time algorithm for a different problem and reduce the clique problem to that problem).
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2. For a given graph G, we say that H is a clique if H is...
2. For a given graph G, we say that H is a clique if H is a complete subgraph of Design an algorithm such that if given a graph G and an integer k as input, determines whether or not G has a clique with k vertices in polynomial time. (Hint: Try to first find a polynomial time algorithm for a different problem and reduce the clique problem to that problem).
X) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k ...
COMP Discrete Structures: Please answer completely and
clearly.
(3).
(5).
x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...
1) Consider the clique problem: given a graph G (V, E) and a positive integer k, determine whethe...
1) Consider the clique problem: given a graph G (V, E) and a positive integer k, determine whether the graph contains a clique of size k, i.e., a set of k vertices S of V such that each pair of vertices of S are neighbours to each other. Design an exhaustive-search algorithm for this problem. Compute also the time complexity of your algorithm.
(a) Given a graph G = (V, E) and a number k (1 ≤ k ≤...
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2. For a given graph G, we say that...
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COMP Discrete Structures: Please answer completely and
clearly.
(3).
(5).
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