t11 - color : V → { 1 , 2 , 3 } such that for all ( v, w...

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CS3230 Tutorial 11 1. Show that the question of determining whether a graph G = ( V, E ) has a simple cycle of size at least k is NP-complete. 2. Consider the following problem called vertex cover. Input: An undirected graph G = ( V, E ), and a number k . Question: Does there exists a vertex cover of size k ? That is, does there exist V 0 V , | V 0 | ≤ k such that, for each edge ( u, v ) E , at least one of u, v is in V 0 . Show that the above problem is NP complete. 3. 3-Colorability Input: An undirected graph G = ( V, E ). Question: Is there a mapping
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Unformatted text preview: color : V → { 1 , 2 , 3 } such that for all ( v, w ) ∈ E , color ( v ) 6 = color ( w )? Show that the above problem is NP-complete. 4. Not-All-Equal SAT (NAESAT). Input: A set of variables V , and a set C of clauses (you may assume each clause has exactly three literals). Question: Is there a truth assignment to the variables so that each clause has at least one true literal and at least one false literal? Show that the above problem is NP complete. 1...
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