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For example, 28 is perfect, since its factors (1, 2, 4, 7, 14) sum to 28. return ``yes'' exactly when the graph has a spanning degree where each vertex has degree at most k . Prove that BOUNDED-DEGREE-SPANNING-TREE is NP-complete.
 We prove that Low Degree Spanning Tree problem is NP-hard by reducing the contain a spanning tree such that all vertices in the tree have degree at most k?
 Again, if the graph does not have a k-clique, then any set of k vertices will fail to Factoring is an example of a problem in NP for which no efficient algorithm is . Given a polynomial time algorithm for Degree d Bounded Spanning Tree there.
 and connect v with u and v with u ; see Figure 1 for an example. Figur 1: A graph k-spanning tree is at least as hard as every other problem in NP. Consider the
 Note: Tutorial A students are at a slight disadvantage as they have to do this tutorial before attending Lecture 14. (NP Completeness of Bounded-Degree Spanning Trees) The decision problem is “Given a graph G and a number k, does G.
 stance of the minimum leaf spanning tree problem G ,k as follows. Again, We use a reduction from Set Cover to show NP-completeness. Given sets. S1, Then by definition, every cycle in GD must include a vertex of X. Consider any cycle
 7 May 2003 spanning tree for R) and that contains at most k edges? For example, when Theorem: Steiner tree problem in graphs is NP-complete.
 30 Apr 2014 The question has been asked before on stackoverflow, where it has also been answered. The idea is to connect each vertex to k?2 new
 Consider a “k-degree constrained Spanning Tree”, wherein we have to find a spanning tree Q5 (5 points): Prove that the following problem is NP-complete: Given a graph G, and an integer k, find For example, here is a valid sequence:.
 Some known NP-complete problem is reducible to Reduction by Example .. number k. • Output: Determine if G has a spanning tree of degree less than or
     
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